To simplify $6c + 4d - c - 7d$, we combine like terms:

1. Combine the $c$-terms: $6c - c = 5c$
2. Combine the $d$-terms: $4d - 7d = -3d$

Thus, the simplified expression is:

$5c - 3d$

Let me know if you would like further explanation or details! Here are some related questions:

1. How can I factor an expression like this?
2. What are some practical applications of simplifying expressions?
3. How does the distributive property relate to combining like terms?
4. Can you explain why coefficients are added or subtracted directly?
5. How would this change if variables were multiplied instead of added?

Tip: Always group and simplify like terms carefully to avoid errors.