The image you've uploaded contains a geometric problem with three lines (g1, g2, and g3) and two points (A and B) marked on the graph. The problem asks to determine the coordinates of points A and B, given the equation for line g2: $y = x + 2$, and that lines g2 and g3 are parallel.

Observations:

1. g2 is the line $y = x + 2$, meaning its slope is 1 and its y-intercept is 2.
2. g3 is parallel to g2, so it will have the same slope (1), but we need to determine its equation by finding its y-intercept using a point on g3.
3. g1 appears to be a horizontal line at $y = 8$.
4. The coordinates of point A and point B need to be determined.

Step-by-step solution:

1. Equation of line g3: Since g2 and g3 are parallel, they both have the same slope of 1. Let the equation of g3 be $y = x + c$, where $c$ is the y-intercept. From the graph, it seems that line g3 passes through the point (0, 12). Substituting this into the equation of g3: $12 = 0 + c \implies c = 12.$ Therefore, the equation of g3 is $y = x + 12$.

2. Finding the coordinates of point A: Point A is where lines g2 and g3 intersect. To find the coordinates of A, we set the equations of g2 and g3 equal to each other: $x + 2 = x + 12.$ Solving this equation gives: $2 = 12, \text{ which is not possible.}$ Therefore, there seems to be an issue here. Let me know if you'd like me to adjust the assumptions or solve using another method!