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2\left(z+3\right)+h\left(z+3\right)
Do the grouping 2z+6+zh+3h=\left(2z+6\right)+\left(zh+3h\right), and factor out 2 in the first and h in the second group.
\left(z+3\right)\left(2+h\right)
Factor out common term z+3 by using distributive property.