The mains has a frequency of 50 Hz and an rms voltage of 230 V…

Step 1. The peak value. $V_m = \sqrt{2} \times 230\ \text{V} = 325$ V.

Step 2. The rms voltage. We want $v = 230$ V, so $\sin \omega t = \dfrac{230\ \text{V}}{325\ \text{V}} = 0.707$. That is $\omega t = 45^\circ$. This is $\dfrac{45^\circ}{360^\circ} = \dfrac{1}{8}$ of the period, so $t = \dfrac{20\ \text{ms}}{8} = 2.5$ ms.

Step 3. Half of the peak. Now $\sin \omega t = 0.5$, so $\omega t = 30^\circ$. This is $\dfrac{1}{12}$ of the period, so $t = \dfrac{20\ \text{ms}}{12} = 1.67$ ms.