It's obvious from the graph that the x-intercept is (3,0). Thus, when x=3, y=0. We can use this fact to eliminate those of the 4 possible answers that could not be correct. Note that log (1) = 0.
Eliminate the first answer: log(x + 4). Why? Because when x=3,
log(x + 4)=log(3 + 4)= log 7, which is NOT zero.
Elim. the second answer for the same reason.
Next, look at the third answer: log(x + 4). If x=3, we get log(7), which is not zero.
That leaves only the fourth answer choice. But check that out also:
f(x) = -4log(-x + 4). When x=3, we get f(3)= -4log(-x + 4) = -4(log[1]) = 0. This is correct.