To translate an equation/function down in the vertical direction, you subtract the distance translated down.
Since the equation [tex] f(x)=4x^{2}+6[/tex] is being translated 4 units down, subtract 4 from [tex] f(x) [/tex] to get:
[tex] g(x) =4x^{2}+6-4\\g(x)=4x^{2}+2[/tex]
