Let y = px^2 - 6x + q

Im assuming you know differentiation here.

dy/dx = 2px - 6.
To find the min/max point, we let dy/dx = 0
So, we get that x = 3/p.

Now, we substitute that into y, and we get
y = 9/p - 18/p + q
y = -9/p + q
We want to find sets of values of p and q such that y = 8 is the min or max point.

So, we let y = 8.

So, 8 = -9/p + q
q = 8 + 9/p

Suppose we let p = 1 , q = 17. This is for the lowest point where y = 8.

Suppose now, we let p = -1, q = -1. This is for the highest point where y = 8.

Recall that if the coefficient of x^2 is positive, the curve looks like a smiley face, hence, it will have a lowest point.
Similarly, when the coefficient of x^2 is negative, the curve looks like a sad face, hence it will have a highest point.