The problem asks to find the values of $m$ for which the function $f(x) = (3m-6)x + 2m+3$ is an increasing function.

1. Problem Description

The problem asks to find the values of $m$ for which the function $f(x) = (3m-6)x + 2m+3$ is an increasing function.

2. Solution Steps

A linear function $f(x) = ax + b$ is increasing if and only if the coefficient $a$ of $x$ is positive, i.e., $a > 0$. In this case, $a = 3m - 6$.

So, we require $3m - 6 > 0$.

We solve this inequality for $m$:

$3m - 6 > 0$

$3m > 6$

$m > \frac{6}{3}$

$m > 2$

3. Final Answer

The function $f(x)$ is an increasing function when $m > 2$.