Solution: as shown on the right, connect EF, FG, GH, EH,

E and h are the midpoint of AB and DA, respectively,

Eh is the center line of △ABD,

∴EH= 1？ 2? BD=3，

Similarly, EF, FG and GH are the median lines of △ABC, △BCD and △ACD respectively.

∴EF=GH= 1？ 2? AC=3，FG= 1？ 2? BD=3，

∴EH=EF=GH=FG=3，

∴ The quadrilateral EFGH is a diamond,

∴EG⊥HF, the vertical foot is O,

∴EG=2OE,FH=2OH，

At Rt△OEH, according to Pythagorean theorem: OE? +Oh? = eh? =9,

Multiply both sides of the equation by 4:4OE at the same time? +4OH？ =9×4=36,

∴(2OE)？ +(2OH)？ =36,

Is that EG? +FH？ =36.

So the answer is: 36.