1. **State the problem:** We need to find the equation of the directrix of the parabola given by $$y^2 + 4y + 4x + 2 = 0.$$ 2. **Rewrite the equation:** Group the $y$ terms to complete the square: $$y^2 + 4y + 4x + 2 = 0 \\ y^2 + 4y = -4x - 2.$$ 3. **Complete the square on $y$: ** Add and subtract $(\frac{4}{2})^2 = 4$ on the left side: $$y^2 + 4y + 4 = -4x - 2 + 4 \\ (y + 2)^2 = -4x + 2.$$ Rewrite as $$ (y + 2)^2 = -4(x - \frac{1}{2}).$$ 4. **Identify the parabola form:** The equation is now in the form $$(y - k)^2 = 4p(x - h),$$ where vertex is at $(h, k)$ and $p$ is the distance from the vertex to the focus (and to the directrix). Here, $$h = \frac{1}{2}, \quad k = -2, \quad 4p = -4,$$ so $$p = -1.$$ Since $p<0$, the parabola opens to the left. 5. **Find the directrix:** The directrix is a vertical line $x = h - p$: $$x = \frac{1}{2} - (-1) = \frac{1}{2} + 1 = \frac{3}{2}.$$ **Final answer:** The equation of the directrix is $$\boxed{x = \frac{3}{2}}.$$