To add the polynomial expressions \( 2r^2 - 3r + 4 \) and \( -2r^2 + 3r + 6 \), you can combine like terms.
Here’s the step-by-step addition:
1. Write the expressions:
\[
(2r^2 - 3r + 4) + (-2r^2 + 3r + 6)
\]
2. Combine like terms:
- For \( r^2 \) terms: \( 2r^2 + (-2r^2) = 0 \)
- For \( r \) terms: \( -3r + 3r = 0 \)
- For constant terms: \( 4 + 6 = 10 \)
Putting it all together, we have:
\[
0 + 0 + 10 = 10
\]
So, the sum of the two polynomial expressions is:
\[
\boxed{10}
\]