Are you dealing with the Group as a group or are you dealing with the individuals of the group. You could do as Richard did, identify the client an an Entity, then if you wished add a field to identify the Entity as an Individual, Group or Authorized Person. Similarly with the Project. The Project could simply be ProjectID and ProjectName with an added field to identify the type of project (Designing, Project Management, or Interior Design) Of course, you will need the linking field in your table.
HTH  John
ps: I did this with my own Christmas card list. The Entity is the Family name, then each family may have members (1,2 etc)

Thanks! Could you guide me to content which could help?

Association
Have a look at the videos and see if this will give you an idea as to how you wil like to move on this.

Thanks

I have seen a video where a value was not found in the list behind, we opened the link and added the data and made sure on return the value was assigned to the field. Please help!

Relational Combo

Too Many Tables

Take a look at Rick's ABCD  ABCD  I think Part 1 covers Entity

John

I have watched those recommended videos. I am now able to solve the problem of a person as a customer or a company as a customer. But, When there are two or more people as a customer is what I am looking for! Is there a way out for it?

Whomever you bill your invoices to, that's the "customer" you need to enter into your customer table.  If you bill to Peter, Paul, and Mary separately, then you enter them as 3 customers in your database.  If you bill to "Peter, Paul, and Mary Incorporated", as one entity, then you treat it as one entity.  If they do business both as a company and as 3 individuals, then you enter them that way in your database.  This is more of a business issue rather than an Access technical issue.  When you do business with someone, you always ask, who and where should I bill to, or who should I pay to.  Each customer should have just one bill-to.  If a company does business under two names with two different bill-tos, they become two customers to you, and you enter them accordingly in your table.  

Kashif Bakkar: "I have seen a video where a value was not found in the list behind, we opened the link and added the data and made sure on return the value was assigned to the field. Please help!"

I think the video you might be thinking of is the Association 5 and it's Extended Cut.