Question 6.9: Calculate the volume, in liters, of water that must be added...

Step 1. Summarize the information provided in the problem:
M_1 = 12.0  M \\ M_2 = 0.100  M \\ V_1 = 20.0  mL  (0.0200  L) \\ V_2 = V_{final}

Step 2. Then, using the dilution expression:
(M_1)(V_1)=(M_2)(V_2)

Step 3. Solve for V_2, the final volume:
V_2 = \frac{(M_1)(V_1)}{M_2}

Step 4. Substituting,
V_{final} = \frac{(12.0  M )(0.0200  L)}{0.100  M } \\ \qquad    = 2.40 L M  solution
Note that this is the total final volume. The amount of water added equals this volume minus the original solution volume, or
2.40 L – 0.0200 L = 2.38 L water