15. (6 points) The sum of the unit digit and the tens digit of a certain two-digit number is 12. After swapping the unit digit and the tens digit, the resulting two-digit number is 36 less than the original number. The original number is $\qquad$
【Analysis】Let the unit digit be $x$, then the tens digit is $12-x$, so we can get: the original two-digit number is $10(12-x)$ $+x$, and the new two-digit number after swapping the positions is $10 x+12-x$; according to the new number being 36 less than the original number, we can set up an equation to solve the problem.

【Solution】Let the unit digit be $x$, then the tens digit is $12-x$,
the original two-digit number is $10(12-x)+x$,
the new two-digit number after swapping the positions is $10 x+12-x$; according to the problem, we can set up the equation:
$10(12-x)+x-(10 x+12-x)=36$,
$$
\begin{aligned}
18 x & =72, \\
x & =4 ;
\end{aligned}
$$
$12-4=8$,
Answer: The original number is 84.
Therefore, the answer is: 84 .