A priori, an average of 6 is in the realm of possibility if it's a total fertility rate. Two decades ago the highest national-level European TFR was in Kosovo, where Albanian women had a TFR around 6.5. So Muscovite Tatar women having a TFR of 6 nowadays could be just about possible.

I have a hard time, though, believing that Muscovite Chechen & Ingush women are breaking double digits; that'd be off the national charts. One miiiiight be able to bend over backwards to explain that away as a Moscow-and-ethnicity-specific anomaly, but I'm not sure how.

I poked around a bit to try uncovering more data on Tatar women in Moscow, but couldn't find anything quickly on Google Scholar which had Moscow-specific TFRs by ethnicity. One paper does use 1989 census data to find that in Russia as a whole, ethnic Russian & Tatar women aged 50-54 averaged 1.88 & 2.65 "children ever born" respectively. 2.65 is a lot lower than 6, so either (1) Moscow Tatars are astoundingly prolific compared to Tatars elsewhere in Russia; (2) Russian Tatar women have most of their babies post-menopause; (3) Russian Tatar women, reversing their earlier demographic transition, have more than doubled their TFR in the last 25 years; or (4) "In Moscow, Tatar women have six children [...] on average" is BS. A blog post with blunter but more recent data is suggestive of (4).

Quiverfull people self-select into having lots of children. Women of a particular ethnic background do not.