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:

1. **Identify like terms**:
- \(2r^2\) and \(-2r^2\)
- \(-3r\) and \(3r\)
- \(4\) and \(6\)

2. **Add the coefficients of like terms**:
- For \(r^2\): \(2r^2 + (-2r^2) = 0r^2\)
- For \(r\): \(-3r + 3r = 0r\)
- For the constant terms: \(4 + 6 = 10\)

3. **Combine all the results**:
- \(0r^2 + 0r + 10 = 10\)

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

\[
10
\]