Digits of age

The product of the digits of Andrew age as 6 years ago and not equal to 0. Andrew's age is also the youngest possible age with these two conditions. After how many years will the product of the digits of Andrew age again the same as today?

Correct answer:

n =  18

Step-by-step explanation:

$$\begin{gathered} x=24-6=18 \\ {x}_1=24 \\ {x}_2=2\cdot 4=8 \\ {x}_3=1\cdot 8=8 \\ y=42 \\ {y}_1=4\cdot 2=8 \\ n=y-24=42-24=18=18 \end{gathered}$$

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