The number is -16.
Work Step by Step
"Product" indicates multiplication. "Twice" is multiplication by 2. "Difference" indicates subtraction. Since the difference is a factor in the multiplication, the subtraction is done first so is written in parentheses. $3x=2(x-8)$ $\longrightarrow$distributive property $3x=2x-16$ $\longrightarrow$addition property $3x-2x=2x-16-2x$ $\longrightarrow$combine like terms $x=-16$