The overlapping dates is going to be an issue. Are you saying there are 2 acting presidents at one time? Or that non-active presidents give awards?

I don't think this is something you do in a query though to start with. Doing a calculation to determine which president gave which award over 1.3million records, every time you run the query, is going to be horridly slow. I would add a field to the award table for which president gave the award, and then use a recordset to set the values of that field, it would be a long running recordset but it's only a one-time kind of thing. Once you have that data in a table you can make a query to work with the data however you want.

Korea has had a turbulent history.
One president was up on corruption charges and was not allowed to do her official duties until the investigation was over, so you had an acting president while there was still a president in office. When the president was convicted, the acting president continued in the presidential capacity. Officially, her presidency did not finish until the conviction. There was also a military dictatorship where the general holding the real power kept a president in office, until he fully officially took over.
One issue that I have is that the Award Table is a living/breathing entity that is officially updated every three months.
As far as the wait time, this is a hobby pursuit, I'm retired, so I have the time. I just don't know how to query a count with two separate date fields. Also I could run each active/acting president separately, which should cut down the wait time, and that is the result that I am really looking for.

So what are you wanting to happen when you have an award given that has 2 acting presidents during that time range? Access won't be able to figure out who was in trouble or who gave the award, is there some other criteria available?

What I am looking for is to count the number of awards per president. Even if the terms in office overlap, it really shouldn't matter. I just need to get the total count of awards between this date and this date.

If President A served 1/1/2000 to 1/1/2004 and President B served 1/1/2003 to 1/1/2005

Award 1 was given on 6/6/2000
Award 2 was given on 6/6/2002
Award 3 was given on 6/6/2003
Award 4 was given on 6/6/2004

President A would have given 3 awards (1,2,3) and President B would have given 2 awards (3,4). Award 3 is given by two presidents in this case. Is that fine or how do you want to handle that? Once I'm sure I understand how you want to add up the numbers I can help you make something to do it.

The same award given by two presidents is okay. President A with 3 awards and President B with two awards, totaling 5 awards when there are only 4, is not a problem. Once I know how to do the query, I can refine it sometime down the road to show how much overlap.
I appreciate you taking the time to help me.
Don

I would suggest you enter the overlapping periods as separate entries in your table.  For instance:

PresidentName                 StartedOffice  LeftOffice
Park Geun-hye                 2013-02-25     2016-12-08
Park Geun-hye/Hwang Kyo-ahn   2016-12-09     2017-03-10
Hwang Kyo-ahn                 2017-03-11     2017-05-09

One entry for President Park serving alone.  A separate entry for Park and Hwang serving together (when Park was being impeached).  Another entry for Hwang serving alone (after Park was convicted and removed from office).  That way you will get accurate counts, because there is no overlapping of the dates in your table.  That is the trick.  Even when there is overlapping in real life, you can get rid of the overlapping by treating the overlapped period as a separate entity.

Just my two cents, if I may!!  To possibly provide improved accuracy while accounting for overlapping time periods and changes in official positions, I suggest the following 3 tables with appropriate relationships applied of course ;)!!

PresidentT (or "OfficeHolder"T)
PresidentID   PresidentName
1                  Le Myung-bak
2                  Park Geun-hye
3                  Hwang Kyo-ahn
4                  Moon Jae-in

TermT                
PresidentID     Postion               StartDate         EndDate          
1                    President            02/25/2008     02/24/2013
2                    President            02/25/2013     03/10/2017
3                    Acting President  12/09/2016     05/09/2017
4                    President            05/10/2017     05/09/2022

AwardsGivenT
AwardID     Award               DateGiven       Givenby (PresidentID)
1                Award Abc         06/06/2012       1    
2                Award Cde         06/06/2014       2
3                Award Efg          06/06/2016       2
4                Award Ghi          01/25/2017       3
5                Award Ijk           06/06/2017       4

The easiest way to do it if it doesn't have to be perfectly exact, is to just count the number of awards given during each presidents time period. (Which would result in 5 awards when there are only 4 like my example).

You could do that with a query field, bring in your presidents table, and add another field like (This is still probably going to be slow)
AwardsGiven: DCOUNT("*","AwardsT","AwardGivenDate>=# & PresidentStartDate & "# and AwardGivenDate<=# & PresidentEndDate & "#")

Now if you want to know which award was given by which president, I would do that with a recordset, although it is going to be a LONG running recordset (like walk away and do your taxes long probably). But it lets you use the data instantly in the future, and if it's only one time every 3 months like you said, that's probably OK. You said you want the counts of awards given by each president, so I'm not sure if which awards were given by which presidents is something you care about.

I appreciate your help on this. Got a little tied up today, so I will work on this tomorrow.
Thanks.
Don

Sorry for being such a pest, but I am having issues with the coding.
I changed all the names, double-checked them and double checked the original syntax and entered it into a query.
Now I am getting a 'The expression you entered has invalid syntax You may have entered an operand without an operator'
AwardsGiven: DCOUNT("*","AwardsT","AwardGivenDate>=# & PresidentStartDate & "# and AwardGivenDate<=# & PresidentEndDate & "#")
The first # and AwardGivenDate<=# is not having a problem, but the error focuses/highlights on the 2nd # and AwardGivenDate<=#
Any idea what I am doing wrong?

Your missing quotations on both of the first #, sorry I must have missed that too.

AwardsGiven: DCOUNT("*","AwardsT","AwardGivenDate>=#" & PresidentStartDate & "# and AwardGivenDate<=#" & PresidentEndDate & "#")

Thank you. I was looking at examples on the net and I was leaning towards the quotation marks, but wasn't sure.
Again, Thank you.