420. When dividing a two-digit number by 6, the remainder is equal to the digit in the tens place, and when dividing the same number by 10, the quotient is 3 and the remainder is the digit in the units place of the dividend. Find all such two-digit numbers.
$\triangle$ Let the desired number be denoted by $\overline{x y}$. Then

$$
\left\{\begin{array}{l}
\overline{x y}=6 q+x \\
\overline{x y}=30+y
\end{array}\right.
$$

From the second equation, we get:

$$
10 x+y=30+y, \quad x=3
$$

Transform the first equation:

$$
30+y=6 q+3, \quad 27+y=6 q
$$

From this, the digit $y$ is odd and divisible by 3, i.e., $y=3$ or $y=9$.

Answer: $33,39$.