Explanation:

- We know 200 divided by x leaves a remainder of 8.

- This implies $200\equiv 8(\mathrm{mod}x)$.

- We can rephrase this as $200-8=192$ is divisible by x.

- So, x must be a divisor of 192.

- 192 factors into 2 x 96, 3 x 64, 4 x 48, 6 x 32, 8 x 24, 12 x 16.

- The divisors of 192 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192.

- However, x must be greater than 8 (since the remainder is 8).

- The valid divisors above 8 are: 12, 16, 24, 32, 48, 64, 96, 192.

- The number of such x values is 8.

- So the correct option is 3, which states 8.