PEMDAS (Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction)
Parenthesis
(-4^2) - inside that we do Exponents first. That makes it (-16).
(2^4)=2*2*2*2=16
Next, we have Exponents
3^2=9, 4^2=16, and 2^4=16
Putting that all together so far, we have 2(-16) -2(16) +9 - -16 +16
Taking Multiplication next, we have 2(-16)=-32 and 2(16)=32.
Then, we have -32 - -32 +9 - -16 +16
Making the double negatives positive (-1*-1=1), we get
-32+32+9+16+16
After that, we add -32 and 32 together to get 0, add 16 and 16 to get 32, then add 9 to 32 and get 41.
Congratulations - you got it right!