>>11568925Either there's something missing from that question, or it's simple to the point of triviality.
Assuming it's the second: if L is {10, 111, 010, ...whocares...}, then they want to transform it into L' {##, ###, ###, ...thelasttwoareactuallythesame...}. They present you with a FSA that recognises L, and want you to describe how you'd transform it into a FSA that recognises L'.
I'm not going to do your homework for you, but look at the FSA they gave you. First off, what words does it accept? Write that down, call it L. Now how what would L' look like? Very similar, except with #. Can you now build a FSA that accepts L'?
Once you do this, it's just a matter of generalising your description (if it's not general enough already).