Let’s set up two equations from the given mean and variance:

Mean = 9 ⇒ total sum = 8·9 = 72

Known values sum to 6+4+8+12+10+13 = 53, so

$$a + b = 72 - 53 = 19.$$

Population variance = 9.25 ⇒

$$\frac{\sum x_i^2}{8} - 9^2 = 9.25\quad\Longrightarrow\quad \sum x_i^2 = 8\,(81 + 9.25) = 722.$$

Known squares sum to 6²+4²+8²+12²+10²+13² = 529, so

$$a^2 + b^2 = 722 - 529 = 193.$$

Now use

$$(a + b)^2 = a^2 + 2ab + b^2 \quad\Longrightarrow\quad 19^2 = 193 + 2ab$$

so

$$361 = 193 + 2ab\quad\Longrightarrow\quad ab = 84.$$

Finally,

$$a + b + ab = 19 + 84 = 103.$$

Answer: 103 (Option A).