Add the polynomial

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

1. Add the \(r^2\) terms:
\[
2r^2 + 2r^2 = 4r^2
\]

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

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

Now, combine all these results:
\[
4r^2 + 0r + 10 = 4r^2 + 10
\]

Therefore, the sum of the polynomial expressions is:
\[
\boxed{4r^2 + 10}
\]