Set up your characteristic equation using the quadratic.
\(\displaystyle \L\\m^{2}+4m+8\)
\(\displaystyle m_{1}={\alpha}+i{\beta} \;\ and \;\ m_{2}={\alpha}-i{\beta}\)
Use \(\displaystyle \L\\y=e^{{\alpha}x}\left(C_{1}cos({\beta}x)+C_{2}sin({\beta}x)\right)\)
This has only complex roots: \(\displaystyle \L\\-2+2i \;\ and \;\ -2-2i\)
\(\displaystyle y=e^{-2x}\left(C_{1}cos(2x)+C_{2}sin(2x)\right)\)
Now, using your initial conditions, can you find C1 and C2?.