The coefficient of x⁵ in (2 - x + 3x²)⁶ is

${\left(2-x+3x^2\right)}^6={}^{6}C_0(2-x{)}^6{\left(3x^2\right)}^0+{}^{6}C_1(2-x{)}^5{\left(3x^2\right)}^1+{}^{6}C_2(2-x{)}^4{\left(3x^2\right)}^2+{}^{6}C_3(2-x{)}^3{\left(2x^2\right)}^3+\cdots$

Coefficient of x⁵ is $-{}^6\mathrm{C}_0{}^6\mathrm{C}_{5}2-{}^6\mathrm{C}_1{}^5\mathrm{C}_3{2}^2\times 3-{}^6\mathrm{C}_2{}^4\mathrm{C}_1{2}^3\times 3^2$

$=-12-6\times 10\times 4\times 3-15\times 4\times 8\times 9=-12-720-4320=-5052$.