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To add the polynomial expressions \(2r^2 - 3r + 4\) and \(-2r^2 + 3r + 6\), you combine like terms:
\[
(2r^2 - 3r + 4) + (-2r^2 + 3r + 6)
\]
Now, we can group the terms by their degrees:
1. **Quadratic terms**: \(2r^2 - 2r^2 = 0\)
2. **Linear terms**: \(-3r + 3r = 0\)
3. **Constant terms**: \(4 + 6 = 10\)
Putting it all together:
\[
0 + 0 + 10 = 10
\]
Thus, the sum of the two polynomial expressions is:
\[
\boxed{10}
\]