The problem is straight forward.

We know that the substitution matrix, S, is symmetric. Therefore, b = 2. Furthermore, S is negative semidefinite. So we know that the sign of every odd order principal minor is non-positive and every even order principal minor is non-negative. This then implies that a =< -8, but we do not know its exact value yet.

From here it gets a little trickier. First, we know that the Hicksian demand function is homogeneous with degree 0 in prices (this follows from expenditure minimization problem). By Euler's Theorem, we know then that S * P = 0, where P is a price vector. Because we know that the price of good-one is 8, we have two equations and two unknowns, namely p and a. Hence, we have p = 32 and a = -8.

So we have: a = -8, b = 2, and p = 32.