Select the missing number from the given alternatives in the sequence: 12, 8, 4, 8, 4, 12, 4, 12, 8, 100, 44, ?

Introduction / Context:
This question mixes a simple repeating set of three numbers with an additional set of terms generated by a product based rule. It tests whether you can see not only the repetition of small blocks but also how groups of three numbers can be combined to generate new numbers later in the series. Such sliding window product plus patterns are common in reasoning questions.

Given Data / Assumptions:

• Long series: 12, 8, 4, 8, 4, 12, 4, 12, 8, 100, 44, ?
• The first nine numbers show recurring values 12, 8, and 4 in different orders.
• The last three numbers, 100, 44, and the missing term, are related to the previous triplets.

Concept / Approach:
Notice that 12, 8, 4 appears as a triple, then 8, 4, 12, then 4, 12, 8. These are rotations of the same three values. The numbers 100 and 44 can be compared against the preceding triplets to see if there is a relationship that uses multiplication and addition. A neat pattern is often of the form first * second + third for each group of three consecutive numbers.

Step-by-Step Solution:
Step 1: Take the first three numbers 12, 8, 4 and compute 12 * 8 + 4. 12 * 8 = 96, and 96 + 4 = 100, which matches the tenth term in the series. Step 2: Take the next three numbers 8, 4, 12 and compute 8 * 4 + 12. 8 * 4 = 32, and 32 + 12 = 44, which matches the eleventh term in the series. Step 3: Take the next three numbers 4, 12, 8 and compute 4 * 12 + 8. 4 * 12 = 48, and 48 + 8 = 56. Step 4: Therefore, by applying the same rule first * second + third, the missing twelfth term must be 56.

Verification / Alternative check:
Summarise the pattern using a sliding window of size three: (12, 8, 4) generate 100; (8, 4, 12) generate 44; (4, 12, 8) generate 56. The rule applied consistently is first * second + third. Since all three computations match the actual or required terms, this strongly confirms that 56 is the correct missing number derived from the last visible triplet before the question mark.

Why Other Options Are Wrong:
Options 80, 48, and 36 do not equal 4 * 12 + 8. Using any of these values would break the consistent rule that ties each group of three numbers to a resulting number later in the chain. Since both 100 and 44 align perfectly with the formula, the last result must also follow it for the series to remain logically constructed.

Common Pitfalls:
Some students focus only on the first nine terms and try to guess a direct pattern among them, missing the link between the three number blocks and the later values. Others may attempt to use simple differences, which do not reveal the multiplicative structure here. When groups of three or more repeat, always consider sliding window style operations such as products and sums across each group.

Final Answer:
The missing number that completes the series according to the rule first * second + third is 56.