x^{2} + x + 3 - 4x -4x^{2} - 10

"Like terms" are terms that contain the same variables raised to the same power, such as x^{2}. Only the numerical coefficients are different (3x^{2}, -5x^{2}, etc.). The first step is to group the like terms. I've added parentheses to make it clear, but the parentheses are not required:

(x^{2} - 4x^{2}) + (x - 4x) + (3 -10)

Here x^{2} and -4x^{2} are like terms, x and -4x are like terms, and 3 and -10 are like terms. Next simplify by adding or subtracting the like terms:

x^{2} - 4x^{2} = -3x^{2}

x - 4x = -3x

3 - 10 = -7

x^{2} + x + 3 - 4x -4x^{2} - 10 = (x^{2} - 4x^{2}) + (x - 4x) + (3 -10) =
**-3x**^{2} - 3x - 7