Here is one way.
Remember, you "complete the square" only when the coefficient of the squared variable is 1.
6 +4x -4x^2
= -4x^2 +4x +6
= -4(x^2 -x) +6
Now, complete the square,
= -4(x^2 -x +(-1/2)^2 -(-1/2)^2) +6
= -4[(x -1/2)^2 -1/4] +6
= -4(x -1/2)^2 +1 +6
= -4(x -1/2)^2 +7
= 7 -4(x -1/2)^2 ----------answer.