If you increase a number $X$ by $20\%,$ you get $Y.$ By what percent must you decrease $Y$ to get $X?$
1. Given that increasing a number \( X \) by \( 20\% \) results in \( Y \), we can express this relationship mathematically as:
   \[
   Y = 1.2X
   \]

2. We need to determine the percentage decrease required to reduce \( Y \) back to \( X \). Let \( P \) be the percentage decrease. This means we want to find \( P \) such that:
   \[
   X = Y \times (1 - P)
   \]

3. Substitute \( Y = 1.2X \) into the equation:
   \[
   X = 1.2X \times (1 - P)
   \]

4. Solve for \( P \):
   \[
   X = 1.2X \times (1 - P)
   \]
   \[
   1 = 1.2 \times (1 - P)
   \]
   \[
   1 = 1.2 - 1.2P
   \]
   \[
   1.2P = 1.2 - 1
   \]
   \[
   1.2P = 0.2
   \]
   \[
   P = \frac{0.2}{1.2}
   \]
   \[
   P = \frac{1}{6}
   \]

5. Convert the fraction to a percentage:
   \[
   P = \frac{1}{6} \times 100\% = 16\frac{2}{3}\%
   \]

Conclusion:
\[
\boxed{16\frac{2}{3}\%}
\]