To determine the variance of $X$, we must first determine the variance of $Y$. Expected value $E(Y) = \\sum y \\times P(y) = (0 \\times 0.3) + (1 \\times 0.2) + (2 \\times 0.4) + (3 \\times 0.1) = 0 + 0.2 + 0.8 + 0.3 = 1.3$

Expected value of $Y^2$, $E(Y^2) = \\sum y^2 \\times P(y) = (0^2 \\times 0.3) + (1^2 \\times 0.2) + (2^2 \\times 0.4) + (3^2 \\times 0.1) = 0 + 0.2 + 1.6 + 0.9 = 2.7$

Variance $Var(Y) = E(Y^2) - [E(Y)]^2 = 2.7 - (1.3)^2 = 2.7 - 1.69 = 1.01$

Given $X = 2Y + 10$: According to the properties of variance, $Var(aY + b) = a^2 \\times Var(Y)$. $Var(X) = 2^2 \\times Var(Y) = 4 \\times 1.01 = 4.04$.

The closest option given is 4.