Step 1: Understand candidate votes and total valid votes

The candidate got $9261$ votes which represents $75\%$ of the total valid votes. Let $V$ be the total valid votes.

$0.75 \times V = 9261 \implies V = \frac{9261}{0.75} = 12348$

Step 2: Relate valid votes to total votes cast

Given that $2\%$ of the votes cast were declared invalid, the valid votes are $98\%$ of the total votes cast ($C$).

$0.98 \times C = 12348 \implies C = \frac{12348}{0.98} = 12600$

Step 3: Relate total votes cast to total enrolled voters

Given that $75\%$ of the voters enrolled cast their votes ($E$).

$0.75 \times E = 12600 \implies E = \frac{12600}{0.75} = 16800$

Step 4: Final calculation

Combining all steps into a single expression for total voters enrolled $E$:

$E = 9261 \times \frac{100}{75} \times \frac{100}{98} \times \frac{100}{75} = 16800$