The angle ANB is equal to 90 and AN=BN.

And because AM=BM=4 root number 2.

So the radical number 2 of AB=8

So AB=BN=8 (Pythagorean theorem)

And because angle A= angle b = 45 and angle CMD=45.

So AME angle plus BMF angle = 135.

Because angle AME plus angle AEM = 135.

So angle AEM= angle BMF (equivalent replacement)

So the triangle AEM is similar to the triangle BMF.

So AE: BM = am: BF

That is, 3: 4 root number 2=4 root number 2: BF

BF=32/3

So FN=BN-BF

EN=AN-AE

Then Pythagorean theorem, find EF.

The square of EF = the square of en plus the square of FN

Final prescription

That's the process. As for the result, I have no time to forget it. sorry O(∩_∩)O~