The key phrase is "the product of ... and ..." This indicates that we should multiply two things.
... * ...The two terms that are involved in the multiplication are: "the square of a number" and "8." In case of multiplication order of terms does not matter because of the Commutative Property of Multiplication.
8* a number^2
The phrase "a number" this is indicating an arbitrary number or a variable. If we call this number x, we can complete our expression.
the product of the square ofa number and 8
8 * x^2
Notice that when we multiply a number by a variable we can omit the multiplication sign. Remember that this is only one of multiple ways to algebraically express the given verbal expression.