I think the difficulty of this problem lies in how to determine the function change relationship, that is, how AB+AC changes.

In order to illustrate this problem, a plane rectangular coordinate system as shown in the figure is established: B is the origin, BA is the positive semi-axis of X axis, the perpendicular of AB is the Y axis, and the point M is MH perpendicular to AB. MBA=a, because BM=2√? 3,∠? BAC=60？ Obviously am and BM are functions of a.

AC=2AM=8sina，AB=BH+AH=2sina+2√？ 3 Kossa. AC+AB= 10sina+2√？ 3 Kossa. The maximum value is

√( 100+ 12)=4√7.

This problem should also be solved in polar coordinates.