A stock bottle of nitric acid is 69 % by mass, with a density of 1.41 g/mL…

Step 1. Stock molarity. One litre has a mass of $1000 \times 1.41 = 1410\ \text{g}$. Of this, $69\ \%$ is acid: $0.69 \times 1410 = 972.9\ \text{g}$. Moles: $\dfrac{972.9}{63} = 15.44\ \text{mol}$. So the stock is $15.44\ \text{mol/L}$.

Step 2. Moles needed. $0.100\ \text{mol/L} \times 0.500\ \text{L} = 0.0500\ \text{mol}$.

Step 3. Volume of stock. We want $V_1$. Since $M_1V_1 = M_2V_2$, $V_1 = \dfrac{0.0500\ \text{mol}}{15.44\ \text{mol/L}} = 0.00324\ \text{L} = 3.24\ \text{mL}$.