jmc

We proceed as follows: $$\begin{array}{rl}3y^2+5y+2& =4\\ 3y^2+5y-2& =0\\ (3y-1)(y+2)& =0.\end{array}$$This gives us $y=\frac{1}{3}$ or $y=-2.$ Of these, $y=\boxed{-2}$ is the smaller value, and thus is our answer.