When adding the polynomial expressions 2r^2 - 3r + 4 and -2r^2 + 3r + 6, we combine like terms.
The coefficients of the terms with the same exponent are added together.
The sum of 2r^2 - 2r^2 is 0.
The sum of -3r + 3r is 0.
The sum of 4 + 6 is 10.
Therefore, the sum of the polynomial expressions 2r^2 - 3r + 4 and -2r^2 + 3r + 6 is 0r^2 + 0r + 10, which simplifies to 10.