Answer
$15$
Work Step by Step
We choose where to put the two a's in the six-letter sequence. That is $C(6,2)=\frac{6!}{2!(6-2)!}=\frac{6!}{2!*4!}=\frac{6*5*4*3*2*1}{2*1*4*3*2*1}=\frac{6*5}{2}=15$
The other letters are f's.
This gives a total of $15$ different six-letter sequences that use the letters f,f,a,a,f,f
