If we multiply 32 by 21, we get 672 as the result. If we write the digits of the multiplicand and multiplier in reverse order, then the digits of the product also appear in reverse order (23 × 12 = 276). Let's find other pairs of numbers that have similar properties.
Let $(10 a+b)$ and $(10 c+d)$ be the desired pair of numbers.

$$
(10 a+b)(10 c+d)=10^{2} a c+10(a d+b c)+b d
$$

and

$$
(10 b+a)(10 d+c)=10^{2} b d+10(b c+a d)+a c
$$

We see that the condition is satisfied if

$$
a c<10, \quad a d+b c<10, \quad b d<10
$$

For example, let $a=4, \quad b=2, \quad c=2$ and $d=1$. These four numbers satisfy the desired conditions, so 42 and 21 are a pair of numbers that meet the problem's requirements.

(József Kiss, Pápa.)

The problem was also solved by: Dévai E., Dévai I., Eckstein V., Füstös P., Harsányi Z., Heimlich P., Jánosy Gy., Kepes J., Koffier B., Neumann L., Pichler S., Sárközy E., Schilhanek Gy., Schuster Gy., Steiger J., Tóth B., Viola A., Wottitz R.