write an expression for: the product of 3 and the quantity of a number minus 7

"The product" immediately suggests multiplication; we're going to be multiplying two quantities together, "3" and "a number minus 7"
"A number" just describes an unknown value, so we'll pick the letter n to be that unknown in our expression. "A number minus 7" then could be written as n - 7.
We can now write the product of 3 and (n - 7) as the expression
3 × (n - 7)