A student is thinking of a number - HSC - SSCE Mathematics Standard - Question 9 - 2021 - Paper 1

To begin, we can express the operation described in the question mathematically:

1. The student is thinking of a number, denoted as $x$.
2. The student subtracts 8 from $x$, which can be represented as $x - 8$.
3. This result is then multiplied by 3, giving us $3(x - 8)$.
4. According to the problem, this result is equal to 2 more than $x$, which can be expressed as $x + 2$.

Thus, we can set up the equation:

$3(x - 8) = x + 2$

From the understanding of the problem, the correct equation is option C: $3(x - 8) = x + 2$.