To add the polynomial expressions \( 2r^2 - 3r + 4 \) and \( -2r^2 + 3r + 6 \), we'll combine like terms.
Let's write down the two expressions:
- \( 2r^2 - 3r + 4 \)
- \( -2r^2 + 3r + 6 \)
Now we add them together:
\[ (2r^2 - 3r + 4) + (-2r^2 + 3r + 6) \]
Combine the like terms:
- For \( r^2 \) terms: \( 2r^2 + (-2r^2) = 0r^2 \)
- For \( r \) terms: \( -3r + 3r = 0r \)
- For constant terms: \( 4 + 6 = 10 \)
Putting it all together, we get:
\[ 0r^2 + 0r + 10 = 10 \]
Thus, the sum of the polynomial expressions is \( \boxed{10} \).