During this process, if it reads Y (instead of the symbol a) in state q0, then it implies that all a's have been replaced by X's and hence it needs to check that all b's and c's have also been replaced by Y's and Z's, respectively.
This can be done by entering a state, say q4 and moving the head to right looking for any b's or c's left until the right end is discovered (by reading a blank symbol). If not found, the input is accepted; otherwise it is rejected.
It is observed that at no point the read-write head moves past the extreme left and right symbols, except in the last step when it reads the first blank symbol to the right of w.
This TM can be converted to a LBA by including the two end marks and keeping all the moves except the last one. In the last step when M reads a blank symbol, the LBA will read the right endmarker, > and hence a move of the form 
can be included, where , 
to save the same purpose. This LBA also accepts the same language L as that of M.