the product of a number and -3, increased by 8, is 20.

Explanation:

Step1: Let the number be $x$.

The product of the number and -3 is $-3x$. Then increased by 8 gives $-3x + 8$.

Step2: Set up the equation.

Since $-3x + 8$ is 20, we have the equation $-3x+8 = 20$.

Step3: Solve for $x$.

Subtract 8 from both sides: $-3x=20 - 8$, so $-3x = 12$. Then divide both sides by -3: $x=\frac{12}{-3}=- 4$.

Answer:

$-4$