f(c) means let x=c. Remember that c is just an unknown number.
The expression f(c)=9 means that when we put c through the function f(x)=7-4x, it gives the answer 9. Therefore we know 7-4c=9 is true.
Now we have an equation that we can go through in the normal way:
7-4c=9
-4c=2
4c=-2
c=-0.5