I would:

1. Solve for y' (simply by subtracting 3y)

2. Pick points (t, y) in the t-y plane, and calculate the right-hand-side of the equation.

3. Then for/at each point (t, y), make a little line segment with slope = y'

For example, at the point (0, 0), y ' = -3(0) + (0) + e^(-2*0) = 1

So at the point (0, 0), I would draw a little line segment (not longer than, say 1-1.5 units) with slope ~1.

At the point (0, y), the slope is -3y + 1, so that can help you with step 3, at least for the line t = 0