This is factorable by grouping. One thing to consider is that terms are commutative, meaning they can be rearranged. 

7m + 6mn + 3m² + 14n 

Rearrange terms and group 1st two and 2nd two==> (7m + 14n) + (6mn + 3m²)

From each group, factor out the GCF ==> 7(m + 2n) + 3m(2n + m)

Notice that the quantities in bold are identical (this let's you know you did the technique correctly). So now, the GCF of this new expression is the quantity (2n + m), so let's factor that out.

(2n + m)(7 + 3m) ==> note that if you distribute the bold quantity, you'd get the above expression again.

It looks like you can:

3m² + 6mn + 7m + 14n

3m(m + 2n) + 7(m + 2n)

(3m + 7)(m + 2n)