Add the polynomial expressions 2r2−3r+4

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 \( \boxed{10} \).