Add the polynomial expressions 2r^2 − 3r + 4 and −2r^2 + 3r + 6

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

1. Combine the \(r^2\) terms:
\[
2r^2 + (-2r^2) = 0
\]

2. Combine the \(r\) terms:
\[
-3r + 3r = 0
\]

3. Combine the constant terms:
\[
4 + 6 = 10
\]

Now, putting it all together, we see that the \(r^2\) and \(r\) terms cancel out, and we are left with:
\[
0 + 0 + 10 = 10
\]

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