Digits of age

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

Correct result:

n =  18

Solution:

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

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