f(x+1) means to start with      f(x)=4^x
Put parentheses around the x    f(x)=4^(x)
            Take out the x      f( )=4^( )
Spread the parentheses wide   f(   )=4^(   )
            put in (x+1)      f(x+1)=4^(x+1)

Now take f(x+1)-f(x) and put 4^(x+1) in place of f(x+1)
and put 4^x in place of f(x) and you get

         f(x+1)-f(x)=4^(x+1)-4^x

Then you write 4^(x+1) as 4^x*4^1 then as 4^x*4 then as 4*4^x

         f(x+1)-f(x)=4*4^x-4^x

Then factor out 4^x

         f(x+1)-f(x)=4^x(4-1)
         f(x+1)-f(x)=4^x(3)
         f(x+1)-f(x)=3*4^x

Edwin