Explanation:

- The number 11223344 needs to be arranged such that odd digits occupy odd positions.

- Odd positions (1, 3, 5, 7) need to be filled with the digits 1, 1, 3, and 3.

- The number of distinct arrangements for these odd digits is calculated as:

$$

\frac{4!}{2! \times 2!} = 6

$$

- Even positions (2, 4, 6, 8) are filled with the digits 2, 2, 4, and 4.

- The number of distinct arrangements for these even digits is calculated as:

$$

\frac{4!}{2! \times 2!} = 6

$$

- Multiply the two results to find the total number of distinct 8-digit numbers:

$$

6 \times 6 = 36

$$

- Therefore, the correct option is Option 3: 36.

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