The product of two numbers is 24. The quotient of the two numbers is 6. What are the two numbers?

Let's denote the two numbers as x and y.

From the problem, we have two equations:

1. x*y = 24 (The product of the two numbers is 24)

2. x/y = 6 (The quotient of the two numbers is 6)

We can solve these equations step by step:

Step 1: From equation 2), we can express y in terms of x: y = x/6

Step 2: Substitute y in equation 1) with x/6: x*(x/6) = 24

Step 3: Simplify the equation: x^2/6 = 24

Step 4: Multiply both sides of the equation by 6: x^2 = 144

Step 5: Take the square root of both sides: x = 12 or x = -12 (since the square root of a number can be positive or negative)

Step 6: Substitute x = 12 and x = -12 into equation 2) to find the corresponding y values:

When x = 12, y = 12/6 = 2

When x = -12, y = -12/6 = -2

So, the two pairs of numbers that satisfy the conditions are (12, 2) and (-12, -2).