g(-4) means inputing -4 into x. So you will be replacing x with -4 in order to find a y for that input (-4). So...
g(-4)=-2(-4)^(2) + 1
=8^2 +1
= 64 +1
=65
(btw the question is a bit weird so im assuming that you forgot the exponent sign and it is -2x^2 + 1)