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6\left(a^{3}c-ac^{3}\right)
Factor out 6.
ac\left(a^{2}-c^{2}\right)
Consider a^{3}c-ac^{3}. Factor out ac.
\left(a-c\right)\left(a+c\right)
Consider a^{2}-c^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).
6ac\left(a-c\right)\left(a+c\right)
Rewrite the complete factored expression.