Let's combine the like terms in the expression step-by-step:

Given expression: $6 + 2x^2 - 3y^2 - 7 - 2 - 4x^2 + 4y^2$

1. Combine the constant terms: $6 - 7 - 2 = -3$

2. Combine the $x^2$ terms: $2x^2 - 4x^2 = -2x^2$

3. Combine the $y^2$ terms: $-3y^2 + 4y^2 = y^2$

Now, putting it all together: $-3 - 2x^2 + y^2$

So, the simplified expression is: $-2x^2 + y^2 - 3$

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Would you like further clarification or details on any part of this process? Here are 5 related questions to consider:

1. How do you recognize like terms in an algebraic expression?
2. What happens when you subtract terms with the same variable (like $x^2$ or $y^2$)?
3. How can you factor an expression like $-2x^2 + y^2 - 3$?
4. What are the steps to simplify expressions with more than one variable term?
5. Can you apply this technique to solve for specific variable values?

Tip: Always group and combine terms that have the same variable and exponent before simplifying.