For what value of $a$ does the equation $3(2x-a) = 2(3x+12)$ have infinitely many solutions $x$?
I know that an equation of the form $A = B$ has infinitely many solutions $x$ if and only if $A$ and $B$ are equivalent expressions, that is, they have the same value for all values of $x$. So I want to find out when $3(2x-a) = 2(3x+12)$ is true for all $x$. To do that, I can try to simplify both sides of the equation and see if I can make them equal to each other. On the left side, I can distribute the 3 and get $6x-3a$. On the right side, I can distribute the 2 and get $6x+24$. Now I have $6x-3a = 6x+24$. I can subtract $6x$ from both sides and get $-3a = 24$. To isolate $a$, I can divide both sides by $-3$ and get $a = -8$. This means that when $a = -8$, the equation $3(2x-a) = 2(3x+12)$ has infinitely many solutions $x$. 