Explanation:

- X can complete the work in 46 days. So, X's work rate is 1/46 of the work per day.

- Y can do the work in 92 days. Thus, Y's work rate is 1/92 of the work per day.

- Z can complete the job in 23 days. Therefore, Z's work rate is 1/23 of the work per day.

- X started alone and worked for 2 days. So, work done by X in 2 days = 2 * (1/46).

- After 2 days, Y joined X. So, together they worked for 6 days. The combined work rate is (1/46) + (1/92).

- Then Z joined them after 8 days from the beginning. They worked together until the work was finished. The combined work rate now is (1/46) + (1/92) + (1/23).

- Calculate the total work done to find the number of days X worked, leading up to the completion of the work.

Considering overlap of their contributions and the work rates, let's break it down numerically:

- In the first 2 days, X alone completed 2/46 of the work.

- From days 3 to 8 (6 days), X and Y completed 6*((1/46) + (1/92)) of the work.

- Finally, X worked for a total of 8 more days with Y and Z, contributing an amount until the full task was completed.

- Sum up all partial works to determine completion and verify number of days X participated.

- Let's choose option 3, indicating X worked for a total of 18 days.

Correct Answer: Option 3 (18 days)

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