To find the intersection points of the two curves given by the equations:

y = x² + 4x + 2y = 6

First, substitute y = 6 into equation 1 to get:

6 = x² + 4x + 2
x² + 4x - 4 = 0

Next, solve for x by using the quadratic formula:

x = [-4 ± √(4² - 41(-4))] / 2*1
x = [-4 ± √(16 + 16)] / 2
x = [-4 ± √32] / 2
x = [-4 ± 4√2] / 2

So, x = (-4 + 4√2) / 2 and x = (-4 - 4√2) / 2.

Therefore, the two intersection points are:

(x₁, y) = {((-4 + 4√2) / 2, 6)}(x₂, y) = {((-4 - 4√2) / 2, 6)}