Notice that this product is made up of $2$s and $5$s, and $2\times5$=$10$. Multiplying by $10$ will be useful because multiplying by $10$ increases the number of digits by $1$.

$$\begin{split}2^{18}\times5^{12}&=2^6\times2^{12}\times5^{12}\\

&=2^6\times\left(2^{12}\times5^{12}\right)\\

&=2^6\times\left(2\times5\right)^{12}\\

&=2^6\times10^{12}\\

&=2^6\times10\times10\times ... \times10\end{split}$$

This is $2^6$ multiplied by $10$ twelve times = so $2^6$ with twelve more zeroes afterwards.

$2^6=\left(2^3\right)^2=8^2=64$, which has $2$ digits.

So in total the product has $2+12=14$ digits.

You can find more short problems, arranged by curriculum topic, in our short problems collection.