I’m only 70% positive about my answer, but I believe the answer is A) g(x) = |x+4| - 2.
If I’m correct, the numbers on the inside of the absolute marks are an indication of a horizontal shift of the function and you go the opposite direction of the sign. In this case, it’s a shift to the left (looking at the graph, 4) Then the outside number tells you how far you shift vertically (down 2, following the negative sign this time).