One way to visualize what is going on is to write out each individual term.
$$ 2x^2 \cdot 3x^3 $$
$$ 2 \cdot x \cdot x \cdot 3 \cdot x \cdot x \cdot x $$
$$ \underbrace{2 \cdot 3}_\text{constants}\cdot \underbrace{ x \cdot x \cdot x \cdot x \cdot x}_\text{variables} $$
$$ = \boxed{6x^5} $$
Given exponential terms with the same base, we can multiply by adding the exponents:
$$x^a \cdot x^b = x^{a+b} $$
Accordingly,
$$2x^2 \cdot 3x^3$$
$$2 \cdot 3 \cdot x^2 \cdot x^3$$
$$=6x^{2+3}$$
$$=\boxed{6x^5}$$