Why is my variance negative?

I found my mistake.

$$E(Y_1) = 2$$

$$Var(Y_1) = 2$$

Therefore

\begin{align*} Var(Y_2) = & E\left (Var(Y_2|Y_1)\right) + Var\left ( E(Y_2|Y_1)\right ) \\ = & E \left ( \frac{y^2_1}{12}\right ) + Var \left( \frac{y_1}{2} \right ) \\ = & \frac{6}{12} + \frac{2}{4}\\ = &1 \end{align*}

In addition, the $Cov(Y_1, Y_2) = 3 - (2)\frac{2}{2} = 1$

\begin{align*} Var(Y_1 - Y_2) = &Var(Y_1) + Var(Y_2) - 2 Cov(Y_1, Y_2)\\ = & 2 + 1 - 2(1)\\ = & 1 \end{align*}