Given point B lie on the line x−y−2=0, so the point will be B(x1,x1−2)
Now given distance between AB is 329, so by distance formula,
(x1−4)2+(x1−2−3)2=329
Now on squaring on both side we get,
18x12−162x1+340=0
On solving we get, x1=951 or x1=310
So, y1=933 or y1=34
Now we can see only x+2y=6 will satisfy the point (310,34)