Partial derivatives of 4x^2 - 6xy + 3y^2 -2x -6y +120

need to find
fx(x,y)
fy(x,y)

fx(x,y) = 8x - 6y - 2


fy(x,y) = -6x + 6y - 6

is this right

Yes, your answer is correct. Good work!

PS:
I am assuming that fx(x,y) and fy(x,y) represent the partial derivatives with respect to x and y, respectively.

YES .-