Hi I am trying to work out when I conceived
If your due date is July 6, then, according to calculations, conception must have happened somewhere between October 6 and October 12, because sperm can live inside your body for up to a week. This makes October 8th (the date of intercourse you refer) the most probable date of conception.
I hope this answers your question. Let me know if I can assist you further.
Cycle length needed
I may be able to give you a more accurate answer if you could tell me your approximate cycle length. However, if you did have a period in October that it would be impossible to have ovulated early that month.