In Jain Dharma, there is no scriptural rule that says you cannot wash your head on a certain day of your periods (2nd, 3rd, 6th day etc.).

• Menstruation is a natural process, not a sin.
• Snān (bathing) and cleanliness are always encouraged. You can wash your hair/head on any day of your period according to:

- your health and comfort - your normal hygiene routine

Some families have their own customs like:

• not doing a full head bath during active heavy flow, or
• doing one complete head bath after bleeding stops before going to mandir/doing dravya‑pūjā. ( jainknowledge.com)

These are family/community maryādā, not compulsory Jain Āgamic rules.

So, yes, you may wash your head on the 6th day of your period from a Jain point of view. If your family follows a particular custom, respect it as long as it does not harm your health.

You can read more detailed Jain guidance on this topic here: “Hair wash need need to be done at second day or third day of menstruation?” “When do we need to wash hairs after periods”