As the others have mentioned, you must find the roots or zeroes of the function before solving the inequality. Therefore, the roots for $f(x) =(x-3)(x-2)(x-1)$ are $1,2,3$. There are numerous ways to solve this but I would like to show you how you can do it graphically. Here is the graph of the function:
Note, that the question asks you to find when $f(x) \gt 0$ Therefore, look for all the spots on the graph where the graph is above zero and not equal to zero. Firstly, we can disregard any value that is less than or equal to $1, 2, 3$ because at those points the function is not greater than zero.
Next, we can see from the graph that between the $1$ and $2$, the $f(x)$ is greater than zero. So we can say that one of the solutions is: $$ 1\lt x\lt2 $$ because at points between that interval, the value of $f(x) \gt 0$.
Next, we disregard the interval $ 2 \le x \le 3$ because at that interval $x \le 0$ or in other words, no matter what $f(x)$ you find between that interval, you will always have value that is $\le 0$.
So, all we are left with is $x\gt3$ because according to the graph, all values above $3$ are greater than $0$.
Therefore, the solution through graph analysis is $$1 \lt x \lt 2 \\ x \gt 3$$ or in interval notation $$ (1,2) \cup (3,\infty) $$