If the shortest EF+BF is required, these two line segments should be transformed into a straight line as far as possible.

Just because the diagonal of the diamond is symmetrical on both sides.

So AB focus e and AD midpoint m are symmetrical about line segment AC.

That is MF=EF.

Connect BM and AC at point F, and the segment MB is the minimum value of MF+FB.

Therefore EF+FB=MF+FB=MB.

In the right triangle ABM, MB=AB×sin60? =6×3? /2=3×3?

So the minimum value of EF+FB is 3×3? (3 times the root number 3)