Explanation

Factorising gives x^2 - 7x + 12 = (x - 3)(x - 4), so the inequality is (x-3)(x-4) > 0. A product is positive exactly when both factors have the same sign: both positive (x > 4) or both negative (x < 3). Between 3 and 4 the factors have opposite signs, so the inequality fails there. Hence the solution set is x < 3 or x > 4, option (d).