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

To add the polynomial expressions \(2r^2 - 3r + 4\) and \(-2r^2 + 3r + 6\), 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:

\[
\boxed{10}
\]