1. The problem asks us to find the equation of a function $h(x)$ that first stretches the graph of $f(x) = |x|$ vertically by a factor of 4, then shifts it down by 2 units. 2. The original function is $f(x) = |x|$. 3. Vertical stretching by a factor of 4 means multiplying the function by 4: $$g(x) = 4|x|$$ 4. Shifting the graph down by 2 units means subtracting 2 from the function: $$h(x) = g(x) - 2 = 4|x| - 2$$ 5. Therefore, the equation of the transformed function is: $$h(x) = 4|x| - 2$$ This means the graph is stretched vertically to be 4 times taller and then moved down 2 units on the y-axis.