Exactly 2 g of a coloured solid is dissolved in 200 mL of water…

Step 1. One step. The new beaker gets $\dfrac{20\ \text{mL}}{200\ \text{mL}} = \dfrac{1}{10}$ of the solid, so each step makes the colour $10$ times weaker.

Step 2. (a) After $3$ steps: $10 \times 10 \times 10 = 1000$ times weaker.

Step 3. (b) The masses are $2\ \text{g} \to 0.2\ \text{g} \to 0.02\ \text{g} \to 0.002\ \text{g} \to 0.0002\ \text{g}$. After $3$ steps there is $0.002\ \text{g} = 2\ \text{mg}$, still more than $1\ \text{mg}$. After $4$ steps there is $0.0002\ \text{g} = 0.2\ \text{mg}$.

What it tells us. Even $0.2\ \text{mg}$ can still tint the water a little, so a tiny mass holds a huge number of particles, and each particle is very small.