you need spaces, Double Double Quotes, and DOB if it's a date field needs #

=DMax("SampleDate","tblDatabase","firstname=""" & [firstname] & """ AND DOB=#" & [DOB] & "#")

Thank you so much. That works!!

My tblDatabase has a Yes/No, depending on the hospital. Those with ticks have a different report template. This formula works great for all hospitals with the No option chosen (that is, no tick). If the tick is there, then the formula is not returning the date, but stays blank. Would be grateful for any suggestions.

This is not sufficient information to help you.
What is your table structure?
How are you calling the reports?

Yea like Sami said, we need structure information. The yes/no is not being used as criteria in the formula so it wouldn't affect it. It could be a query not bringing in records on your report under certain criteria or for some reason those fields aren't available on the records with the ticks, could be a lot of things. But probably isn't something we'll be able to answer without some images of the full picture of what's going on. Image Uploads

I am attaching some screenshots here. Just very weird. Some patient, the Dmax works, but not on others. Please see my attached screenshots.

I see a few things wrong with your setup:
    - All your fields are in one Table.
    - Field names starting with a number
    - Field names are not very descriptive.
    - Question mark in one of your field names.

The database is over 15 years old and had very little understanding of relationships back then. For the Dmax, I am only using the firstname and dob for matches. I am still perplexed as to why the Dmax only work for some of the patients, but not all!!

I have narrowed the problem down to the date of birth. DMax seems to work in my database with some dob but not on others, such as 01/09/1999, 10/05/1984...... (UK date format: dd/mm/yyyy).

Finally solved it. It was due to the fact that the sql only recognise the American date system, and not the UK format. The following code works!!
=DMax("SampleDate","tblDatabase","Firstname=""" & [Firstname] & """ AND DOB=" & Format([DOB],"\#yyyy-mm-dd\#"))