24 : 126 : : 8 : ?

Look at the relationship between 24 and 126:

• Check if 24 multiplied by a certain number gives 126:

24×5.25=126

But 5.25 is a decimal, may not be the pattern.

Alternatively check prime factorization:

• 24=4!=1×2×3×4=24
• 126=2×3×3×7=126

Or check if 126 is sum of something like factorial sum or other.

Alternatively, consider the numbers as binomial coefficients or powers.

Also, check whether the number is related to number of factors or something:

24 has 8 factors (1,2,3,4,6,8,12,24) total 8.

126 has factors, but not 24.

Alternatively, consider cube roots or square roots:

Let's try 24²=576, no relation.

Try 24×5.25=126

So for 8:

8×5.25=42

Check 42.

Thus, the answer is 42.

Final Answer: 42