This TM accepts strings w where n_a(w) = n_b(w). Namely, strings where the number of a's is equal to the number of b's (0ax1l State 0: find an 'a' and mark it. Start from front of string (0bb0r (0xx0r (1bb1l State 1: Had found an 'a'. Go back to start of string and look for 'b' (1xx1l (1 2R (2aa2r State 2: Look for a 'b' and mark it. (2xx2r (2bx3l (3xx3l State 3: Have matched a pair of a's and b's. Go back and repeat. (3aa3l (3bb3l (3 0R (0 4l State 4: Ran out of a's. Go back to see if there are no more b's. (4xx4l (4 5l State 5: Final state. The string is all x's.