Write a piece wise function that models this function

The answer is

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Here's how I got that

Start with the piecewise definition for y = |x|.

Everywhere you see an 'x', replace it with x+2

Now tack on "-4" at the end of each piece so that we shift the function down 4 units

Check out the attached images below. In figure 1, I graph y = x-2 and y = -x-6 as separate equations on the same xy coordinate system. Then in figure 2, I combine them to form the familiar V shape you see with any absolute value graph.