Okay, let's think through this step-by-step:
We have a rectangular board with an area of 77 in^2
We want to cut 6 circles out of this board
We want to maximize the area of each circle
To maximize the area of each circle, we need to make the circles as big as possible
The total area of the 6 circles needs to be <= 77 in^2 (the total area of the board)
Let's assume each circle has an area of A in^2
There are 6 circles, so the total area of the circles is 6A in^2
We need: 6A <= 77
A <= 77/6
A <= 12.83 in^2
Therefore, the maximum area of each circle is 12.83 in^2.