To add the polynomial expressions \(2r^2 - 3r + 4\) and \(-2r^2 + 3r + 6\), you combine like terms:
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Combine the \(r^2\) terms: \[ 2r^2 + (-2r^2) = 0r^2 \]
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Combine the \(r\) terms: \[ -3r + 3r = 0r \]
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Combine the constant terms: \[ 4 + 6 = 10 \]
Now, putting it all together, we have:
\[ 0r^2 + 0r + 10 = 10 \]
Thus, the sum of the two polynomial expressions is \(10\).