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

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

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

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

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

Putting it all together, we get:

\[
0r^2 + 0r + 10 = 10
\]

Thus, the sum of the polynomial expressions \( 2r^2 - 3r + 4 \) and \( -2r^2 + 3r + 6 \) is:

\[
\boxed{10}
\]