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Let's factor the given expression:

\[
6m(n - 2) - 7(n - 2)
\]

We notice that \((n - 2)\) is common in both terms, so we can factor it out:

\[
(n - 2)(6m - 7)
\]

Therefore, the fully factored form is:

\[
(n - 2)(6m - 7)
\]

The correct option is **(6m - 7)(n - 2)** (third option).

Would you like further details or have any questions? Here are some related questions:

1. How do you identify common factors in an expression?
2. What is the distributive property in algebra?
3. How can you verify if your factorization is correct?
4. What are the differences between factoring and expanding expressions?
5. How would you approach factorization with more complex terms?

**Tip:** Always look for common factors first before attempting more complex factoring techniques.

Factorise the expression: 6m(n - 2) - 7(n - 2)

Learn how to factor the algebraic expression 6m(n - 2) - 7(n - 2) using the distributive property. This problem explores key algebraic concepts and techniques suitable for students in Grades 8-10.

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