This is a linear differential equation of first order. Solve this by integrating the coefficient of the y term and then raising e to the integrated coefficient to find the integrating factor, i.e. the integrating factor for this problem is e^(6x).
Multiplying both sides of the equation by the integrating factor:
(y')e^(6x) + 6ye^(6x) = e^(12x)
The left side is the derivative of ye^(6x), hence
d/dx[ye^(6x)] = e^(12x)
Integrating
ye^(6x) = (1/12)e^(12x) + c where c is a constant
y = (1/12)e^(6x) + ce^(-6x)
Use the initial condition y(0)=-8 to find c:
-8 = (1/12) + c
c=-97/12
Hence
y = (1/12)e^(6x) - (97/12)e^(-6x)
