Can you help me with this question??

This is a absolute value function, so that means that the vertex is when the graph changes direction.

 

The vertex is at (h, k) h is the opposite of the number inside the absolute value bars (so not 2, but -2). k is the number that is added or subtracted (in this case, -4).

 

So the vertex is at (-2, -4)

 

The axis of symmetry would be what x equals at the vertex. In this problem, the axis of symmetry would be:

 

x = -2

 

Lastly, the parent function is |x|. Without an a value (as is the case in this problem), you can find the transformations just by comparing the vertex of the parent function to the vertex of the problem fucntion. The vertex in the parent function is (0, 0) so that means this graph is shifted two units to the left (left because x is negative in the transformed function), and 4 units down (down because y is negative transformed function).