You just have to choose the 3-element subsets taken from 

the other 6 members

{B,C,D,E,F,G} 

to put with the A to make a 4-element subset
containing the letter A.

That's "6 things Choose 3", written sometimes as 6C3, sometimes 
as C(6,3), and sometimes as .  "The number of combinations of
6 things taken 3 at a time". The formula is 

"Start with 6, write 3 factors 6·5·4 and divide by 3! or 3·2·1"

 = 20
 
Edwin