Question

What is the equation for g(x)?

Answer 1

To translate an equation/function down in the vertical direction, you subtract the distance translated down.

Since the equation $f(x)=4x^{2}+6$ is being translated 4 units down, subtract 4 from $f(x)$ to get:
$g(x) =4x^{2}+6-4\\g(x)=4x^{2}+2$