All four jacks and the two red queens are removed from a pack…

Step 1. Cards left. $4 + 2 = 6$ cards were removed, so $46$ are left.

Step 2. Kings. No king was removed: $P = \dfrac{4}{46} = \dfrac{2}{23}$.

Step 3. Red cards. The red jacks and red queens are $4$ red cards, so $26 - 4 = 22$ red cards are left: $P = \dfrac{22}{46} = \dfrac{11}{23}$.