4. There were plates on the shelf. First, from all the plates except two, $1 / 3$ part was taken, and then $1 / 2$ of the remaining plates. After this, 9 plates were left on the shelf. How many plates were on the shelf?
4. Let's represent the condition of the problem in a drawing

![](https://cdn.mathpix.com/cropped/2024_05_21_e53d4ff4f2278a1c0d12g-031.jpg?height=217&width=886&top_left_y=1162&top_left_x=585)

1) $9 \times 2=18$ (plates) — remain after the first time plates were taken
2) $18-2=16$ (plates) - corresponds to $2 / 3$;
3) $16: 2=8$ (plates) - corresponds to $1 / 3$;
4) $8 \times 3=24$ (plates) - corresponds to all plates minus two;
5) $24+2=26$ (plates) - was.

Answer: 26 plates.