f(x)+x^2+3x+2 is shifted 2 units left. the result is g(x). what is g(x)?

Adding 2 to all the x's shifts the function left.

g(x) = (x+2)² + 3(x+2) + 2

simplify it a bit ...

g(x) = (x+2)² + 3x + 6 + 2

g(x) = (x+2)² + 3x + 8

g(x) = x² + 4x + 4 + 3x + 8

g(x) = x² + 7x +12