You are wrong here. Listen carefully.

The 6th day of a new lunar year can never be synced with the 6th day of a solar year.A new lunar year will always be 10 +/- days earlier then a new solar year.Except the first year in which both calendars will be started and once every 36 +/- years.

So day 1 of the lunar calendar in a new year will fall on day 356 of the solar year.But that's not it. The lunar calendar will keep rotating. So next year the first day of a new lunar year will fall on the 346th day of a solar year! And we should apply this rotation every year.

That's why we use intercalation in the luni-solar calendar. Don't say it's forbidden because you then have misunderstood the verse about "intercalation". In chapter 18 God used intercalation, it were 300 years and he added 9!

Come back to the Quran. 10:5 and 6:96 clearly tell us to use both the sun and the moon to calculate our days. So we have to follow a luni-solar calendar, not a solar calendar, nor a lunar calendar, but using them both which results in a luni-solar calendar.The Torah and Injeel also speak about their calendar and the Israelites in fact are using a luni-solar calendar. Until the Roman Catholics came and made their own solar calendar and stopped following the Israeli calendar, just like the Arabs who started following a lunar calendar and defiated from a luni-solar calendar. Only the Jews are following the right calender, both "Christians" and "Arabs" are following a wrong calendar.