Answer :
Given the equation:
[tex]-3(-8-\boxdot x)-6(x-7)=18x+66[/tex]Let the blank be represented by the letter y.
We can then rewrite the equation as:
[tex]-3(-8-yx)-6(x-7)=18x+66[/tex]First, we open the brackets on the left-hand side.
[tex]\begin{gathered} 24+3yx-6x+42=18x+66 \\ 3yx-6x+24+42=18x+66 \\ (3y-6)x+66=18x+66 \end{gathered}[/tex]Comparing both sides of the equation, we have that:
[tex]\begin{gathered} (3y-6)x=18x \\ \implies3y-6=18 \\ \implies3y=18+6 \\ \implies3y=24 \\ \implies y=8 \end{gathered}[/tex]Therefore, the number which will be used to fill the blank is 8.
That is:
[tex]-3(-8-\boxed{8}x)-6(x-7)=18x+66[/tex]