What does January sixth mean in the Mormon Catholic Church?

There is no such thing as the "Mormon Catholic Church". The Church of Jesus Christ of Latter-day Saints is commonly called the "Mormon" church, and the Roman Catholic Church is usually referred to as the "Catholic Church". They are two different churches.

January 6th is Epiphany and the end of the Christmas season in the Catholic Church, which celebrates Christmas from December 24 to January 6. The Mormon Church typically does not recognize or celebrate Epiphany.