no other month of any year begins on the same day of the week as june: this month and may are the only two months with this property. june ends on the same day of the week as march every year, as each other's last days are 13 weeks (91 days) apart.in common years, june starts on the same day of the week as september and december of the previous year, and in leap years, april and july of the previous year. in common years, june finishes on the same day of the week as september of the previous year, and in leap years, april and december of the previous year.