Can be written as

Find the values of p and q

Here you're being asked to "complete the square" of x^2 + 4x - 8.

1. Take half of the coefficient (4) of x and square it: Square 2: 2^2 = 4

2. Add this result to the given x^2 + 4x - 8, and then subtract the same:

x^2 + 4x - 8 + 4 - 4

3. Rewrite x^2 + 4x + 4 as a perfect square:

(x+2) ^2 - 12

4. Identify p as being 2 and q as being - 12.