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To add the polynomial expressions \(2r^2 - 3r + 4\) and \(-2r^2 + 3r + 6\), you combine like terms.
1. Combine the \(r^2\) terms:
\[
2r^2 + (-2r^2) = 0r^2
\]
2. Combine the \(r\) terms:
\[
-3r + 3r = 0r
\]
3. Combine the constant terms:
\[
4 + 6 = 10
\]
Now, putting it all together:
\[
0r^2 + 0r + 10 = 10
\]
Therefore, the sum of the two polynomial expressions is \(10\).