We know it's an absolute value. The slopes are -1 and 1 so there's no scale factor involved. The right side up V means it's a regular absolute value, not the negation of one. The vertex at the minimum (-4,-2) means our equation must be
y = |x+ 4| - 2
because the argument to the absolute value x+4 must be zero at the minimum (x=-4), and it's value at the minimum must be y=-2.
Answer: A