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t\left(t+2\right)+3k\left(t+2\right)
Do the grouping t^{2}+2t+3kt+6k=\left(t^{2}+2t\right)+\left(3kt+6k\right), and factor out t in the first and 3k in the second group.
\left(t+2\right)\left(t+3k\right)
Factor out common term t+2 by using distributive property.