Add the polynomial expressions 2r2−3r+4

To add the polynomial expressions \(2r^2 - 3r + 4\) and \(-2r^2 + 3r + 6\), we simply combine like terms.

1. Start with the two expressions:
\[
(2r^2 - 3r + 4) + (-2r^2 + 3r + 6)
\]

2. Rearrange and group the like terms:
\[
(2r^2 - 2r^2) + (-3r + 3r) + (4 + 6)
\]

3. Now, perform the addition:
- For the \(r^2\) terms: \(2r^2 - 2r^2 = 0\)
- For the \(r\) terms: \(-3r + 3r = 0\)
- For the constant terms: \(4 + 6 = 10\)

4. Combining these results gives:
\[
0 + 0 + 10 = 10
\]

Thus, the sum of the polynomial expressions is:
\[
\boxed{10}
\]