The product of two numbers is equal to 96, you need to find these numbers if they relate as 2: 3.

Let x be the coefficient of proportionality, then the first number is 2x, then the second number is 3x. The product of these numbers is 2x * 3x. By the condition of the problem, the product of two numbers is equal to 96, then we compose the equation:
2x * 3x = 96;
6x² = 96;
x² = 96: 6;
x = 16;
x = + – √16;
x = + – 4;
x₁ = 4;
x₂ = -4
If x = 4, then 2x = 2 * 4 = 8;
If x = 4, then 3x = 3 * 4 = 12;
If x = -4, then 2x = 2 * (- 4) = – 8;
If x = -4, then 3x = 3 * (- 4) = – 12
Answer: 8 and 12; -8 and -12