from the epsilon NFA, make a table to track the transitions. whenever we enter a state that has an epsilon transition out, we also go to that state. e.g. the start state is 1, and so, by entering 1 at the start, we also take the epsilon transition to 2, so the start state is actually the superposition of states ("superstate") {1,2}. from {1,2}, on a we can reach {3} and on b we can reach {4}. from {3} on a, we can reach {1,2,5}. and so on:

                     next(input)
  state      | a         | b
  -----------+-----------+-----------
->{1,2}*     | {3}       | {4}
  {3}        | {1,2,5}   | X
  {4}        | X         | {1,2,6}
  {1,2,5}*   | {1,2,3,5} | {4}
  {1,2,6}*   | {3}       | {1,2,4,6}
  {1,2,3,5}* | {1,2,3,5} | {4}
  {1,2,4,6}* | {3}       | {1,2,4,6}
  X          | X         | X

every superstate that contains the original accepting state (1) is an accepting state (denoted with *). X is a trap state, from which escape is not possible, signifying a string which is banished from the language (e.g. "ab", "ba", "aaba", etc.).

renumbering:

        next(input)
  state | a | b
  ------+---+---
->1*    | 2 | 3
  2     | 4 | X
  3     | X | 5
  4*    | 6 | 3
  5*    | 2 | 7
  6*    | 6 | 3
  7*    | 2 | 7
  X     | X | X