To find the sum of the two expressions $2x^2 + 4x - 3$ and $6x^2 - 2x + 9$, we add the corresponding terms:

1. Combine the $x^2$ terms: $2x^2 + 6x^2 = 8x^2$

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

3. Combine the constant terms: $-3 + 9 = 6$

Now, summing everything up, we get: $8x^2 + 2x + 6$

Thus, the sum of the two expressions is $8x^2 + 2x + 6$.

Would you like more details or have any questions?

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Here are some related questions:

1. How do you simplify algebraic expressions with more terms?
2. Can you solve for $x$ in $8x^2 + 2x + 6 = 0$?
3. How do you factor quadratic expressions like $2x^2 + 4x - 3$?
4. What is the importance of combining like terms in algebra?
5. How do we solve systems of equations involving quadratics?

Tip: Always group similar terms (like powers of $x$) to simplify expressions efficiently!