Are you asking what the zero function of f(x) is, or are you asking what the zeroes of f(x) are?
If you're asking what the zeroes of f(x) are, then:
2x + 6 = 0
2x = -3
x = -3/2
and
x - 4 = 0
x = 4
the zeroes of f(x) are x = -3/2 and x = 4
Note: I'm providing the answer for 'what are the zeroes of f(x)' because every other question in the algebra 2 section is asking about the 'zeroes of the function f(x)' instead of the 'zero function of f(x)' (which is a bit different).