Video solution:

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Written solution:

Since $20 = 3 \cdot 6 + 2,$ the bottom $2$ letters in each column will occur one more time than the third letter.

This means that the third letter in each column will occur $6$ times, whereas the other $2$ will appear $7$ times.

Using the same analysis, we can see that $R$ and $P$ appear in the third row $7$ times, whereas $Q$ only appears $6$ times.

Therefore, in $20 - 7 = 13$ columns, $P$ and $R$ appear $7$ times, for a total of $13 \cdot 7 = 91$ times.

They also appear $6$ times in $7$ columns, adding $6 \cdot 7 = 42$ appearances to the total. This gives us a total of $91 + 42 = 133$ appearances for $P$ and $R.$

$Q$ will therefore appear $$\begin{align*} 20 \cdot 20 - 2 \cdot 133 &=400 - 266 \\ &= 134 \end{align*}$$ times.

Thus, C is the correct answer.