When the abscissa of point P is x=m, the ordinate y=n=-2m+8.

The straight line y=-2x+8. When y=0 and x=4, then point A (4,0) and AO=4.

s△OAP = OA×n÷2 = 4×(-2m+8)÷2 =-4m+ 16

So: S=-4m+ 16.

2. When S= 12,

12=-4m+ 16

So: m= 1

So: n =-2m+8 =-2x1+8 = 6.

So: the coordinate of point P is (1, 6).