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 can combine like terms:

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

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

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

Putting it all together, the sum of the two polynomials is:
\[
4r^2 + 0r + 10
\]

Since \( 0r \) is essentially zero, we can simplify this to:
\[
4r^2 + 10
\]

So, the final result is:
\[
\boxed{4r^2 + 10}
\]