To add the polynomial expressions \(2r^2 - 3r + 4\) and \(-2r^2 + 3r + 6\), you can combine the like terms.
Here are the steps:
1. **Write the polynomials:**
\[
(2r^2 - 3r + 4) + (-2r^2 + 3r + 6)
\]
2. **Group the like terms:**
- Combine the \(r^2\) terms: \(2r^2 - 2r^2\)
- Combine the \(r\) terms: \(-3r + 3r\)
- Combine the constant terms: \(4 + 6\)
3. **Perform the addition:**
\[
2r^2 - 2r^2 = 0
\]
\[
-3r + 3r = 0
\]
\[
4 + 6 = 10
\]
4. **Combine the results:**
\[
0 + 0 + 10 = 10
\]
So, the sum of the polynomials \(2r^2 - 3r + 4\) and \(-2r^2 + 3r + 6\) is \(\boxed{10}\).