To combine like terms, we need to group terms that have the same variable raised to the same power. Here's the expression:

$y^2 - 2x^2 - 3 - 4$

Now, combine the constant terms $-3$ and $-4$:

$y^2 - 2x^2 - 7$

This is the simplified expression.

Let me know if you need further explanation or more examples! Here are some related questions:

1. What are like terms, and why is it important to combine them in algebra?
2. How do you combine terms with different powers of the same variable?
3. Can you simplify an expression with fractions or negative exponents the same way?
4. What is the process for factoring an expression like $y^2 - 2x^2 - 7$?
5. How do you identify the degree of a polynomial?

Tip: Always check the exponents of the variables when combining terms. Only terms with the same variable and the same exponent can be combined.