4p2 - 12pq - m2 + 9q2

The given expression is $4p^2 - 12pq - m^2 + 9q^2$.
We can rearrange the terms to group the $p$ and $q$ terms together:

$$4p^2 - 12pq + 9q^2 - m^2$$

The first three terms, $4p^2 - 12pq + 9q^2$, form a perfect square trinomial.
Recognize that $4p^2 = (2p)^2$ and $9q^2 = (3q)^2$.
The middle term is $-12pq$, which is $2 \times (2p) \times (-3q)$.
So, the trinomial can be factored as $(2p - 3q)^2$.
The expression becomes:

$$(2p - 3q)^2 - m^2$$

The expression is now in the form $A^2 - B^2$, where $A = (2p - 3q)$ and $B = m$.
The difference of squares formula is $A^2 - B^2 = (A - B)(A + B)$.
Substitute $A$ and $B$ into the formula:

$$((2p - 3q) - m)((2p - 3q) + m)$$