smc

From the units digit calculation, we see that the units digit of $a\times 3$ is $9$. Since $0\le a\le 9$ and $a$ is an integer, the only value of $a$ that works is is $a=3$. As a double-check, that does work, since $23\times 3=69$, which is the first line of the multiplication. The second line of the multiplication can be found by doing the multiplication $23\times b=92$. Dividing both sides by $23$ gives $b=4$. Thus, $a+b=3+4=7$, and the answer is $\boxed{7}$.