Explanation:

Let's break down the information:

- 10% of the voters did not vote.

- 10% of the votes cast were invalid.

- Winning candidate got 56% of the valid votes.

- Margin of victory was 1,458 votes.

Let's calculate starting from:

- Assume total voters = $x$.

- Votes cast = 90% of $x$.

- Valid votes = 90% of votes cast = 81% of $x$.

The winning candidate got 56% of valid votes, which is $0.56\times 0.81x$.

The losing candidate got $0.44\times 0.81x$.

The difference (margin) is given as 1,458:

$$0.56\times 0.81x-0.44\times 0.81x=1,458$$

$$0.12\times 0.81x=1,458$$

$$0.0972x=1,458$$

$$x=\frac{1,458}{0.0972}=15,000$$

- Option 1: 14,000 does not satisfy the margin condition.

- Option 2: 15,000 satisfies all conditions.

- Option 3: 16,000 exceeds the needed total.

- Option 4: 13,000 is below the needed total.

Therefore, the total number of voters enrolled in the voter list is Option 2: 15,000.

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