To find out how many middle schoolers prefer puzzle video games, you can multiply the total number of middle schoolers by the percentage that prefer puzzles.
The total number of middle schoolers is 800, and the percentage that prefers puzzles is 22%.
\[ \text{Number of middle schoolers who prefer puzzles} = 800 \times \frac{22}{100} = 800 \times 0.22 = 176 \]
Therefore, 176 middle schoolers said that they like puzzle video games the best.