Let us solve the matching problem by simplifying the expressions from Column A and finding their matches from Column B.

Simplifying Column A:

1. $6x - 5 - 12x$:
   Combine like terms:
   $6x - 12x = -6x$, so the expression becomes:
   $-6x - 5$.
   Match this to b) $-6x - 5$.

2. $7x + 8x + 10x - 2$:
   Combine like terms:
   $7x + 8x + 10x = 25x$, so the expression becomes:
   $25x - 2$.
   None of the options match, so no answer for this one.

3. $2x - 5x + 8 - 7x$:
   Combine like terms:
   $2x - 5x - 7x = -10x$, so the expression becomes:
   $-10x + 8$.
   Match this to a) $-10x + 8$.

4. $-6 + 9x - 2 - 13x$:
   Combine like terms:
   $9x - 13x = -4x$ and $-6 - 2 = -8$, so the expression becomes:
   $-4x - 8$.
   Match this to d) $-4x - 8$.

Final Matches:

1. b) $-6x - 5$
2. No match.
3. a) $-10x + 8$
4. d) $-4x - 8$

Would you like further clarification or detailed explanations?

Related Questions:

1. How do you combine like terms in algebraic expressions?
2. Can a single expression in Column A have no matches in Column B?
3. What steps can help simplify larger expressions like $7x + 8x + 10x - 2$?
4. How do you identify common terms when dealing with negatives in expressions?
5. How can distributing terms (if necessary) simplify expressions further?

Tip:

Always double-check for common terms when simplifying; organize variables and constants separately before combining them!