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To add the polynomial expressions \( 2r^2 - 3r + 4 \) and \( -2r^2 + 3r + 6 \), we will combine like terms.
1. Start by writing down the polynomials:
\[
2r^2 - 3r + 4
\]
\[
-2r^2 + 3r + 6
\]
2. Now, combine the like terms:
- For the \( r^2 \) terms:
\[
2r^2 + (-2r^2) = 0
\]
- For the \( r \) terms:
\[
-3r + 3r = 0
\]
- For the constant terms:
\[
4 + 6 = 10
\]
3. Putting it all together, we get:
\[
0 + 0 + 10 = 10
\]
Thus, the sum of the two polynomial expressions is \( \boxed{10} \).