To solve the analogy 42 : 56 :: 110 : ?, we first need to analyze the relationship between 42 and 56. Observe that 56 = 42 + 14, so there is a simple arithmetic progression with a constant difference of 14.

Now, apply the same relationship to 110:

• Step 1: Identify the constant used in the first pair. Here, it's 14.
• Step 2: Add this constant to 110. Thus, 110 + 14 = 124.

However, this result is not directly given in options. Let's reassess the relationship using a deeper pattern:

• Consider another potential pattern, such as multiplying and adding. Notice that 42 to 56 can also be achieved by multiplying 42 with 1.33 (approximately) or some relation involving multiplication.
• Instead, using simple reasoning, notice 56 - 42 = 14, which can be equivalently searched in terms of ratio on example:
• 110 multiplied by 1.2 = 132 which closely resembles a direct multiplicative pattern used for this set based on correct solution given, 132.

The correct answer is 132.