(x^2 + 2x - 3)(4x^2 - 5x + 6)
x^2(4x^2 - 5x + 6)
4x^4 - 5x^3 + 6x^2
now the 2nd number
2x(4x^2 - 5x + 6)
8x^3 - 10x^2 + 12x
now the 3rd number
-3(4x^2 - 5x + 6)
-12x^2 + 15x - 18
now put them all together
4x^4 - 5x^3 + 6x^2 + 8x^3 - 10x^2 + 12x - 12x^2 + 15x - 18
combine like terms
4x^4 + 3x^3 - 16x^2 + 27x - 18 <== your answer