Can a wife be taken back after a divorce that occurred six months ago, in which no intercourse took place, knowing that the spouses did not leave the home?

As long as you took your wife back during her iddah (waiting period) from a revocable divorce, she has returned to your marital bond. The validity of the return does not depend on intercourse. Rather, the fundamental principle for a return is through verbal declaration. So, if you uttered the words of return, it is valid.