6 Year Old
The NHS states that children aged 6 to 12 require nine to twelve hours of sleep (but EdPsychEd's graphic suggests roughly nine to eleven hours, so there's some wiggle room).
Aim for a minimum of 10.5 hours each day when working with a child in elementary school.
The majority of six-year-olds attend school, therefore the amount of time they need to get ready for school usually determines when they wake up.
Your child should get up at around 7 a.m. if they have to be at school by 8 a.m. and need an hour to get ready. Thus, a six-year-old's bedtime should be approximately eight o'clock at night. Make any necessary adjustments to ensure that everything works with your timetable.
Try pushing back your child's bedtime by 30 minutes to see if that helps if they are still exhausted.