From experience, six year olds get very excitable at birthday parties! I’ve found what works best are lots of party games, but nothing too babyish because at that age they’re desperate to be ‘big kids’.
Strawberry shoe lace race: competitors put one end of a strawberry shoelace between their lips and then put their hands behind their back. Somebody else shouts go and all competitors race to get the shoelace into their mouth without using their hands.
After Eight Race: similar to the shoelace race but start with an After Eight on forehead and it's the first player to get it in the mouth.
Doughnut on a string: another eating with no hands race, this time with doughnuts hanging on a piece of string!
Post it shake: This fun game has the easiest set-up. All you need are post-it notes and a timer. First, have the players split up into groups of two or three. One child will stand still while their teammates cover them with as many post-its as they can. Once the timer goes off, count how many post-its are on each player. The team that has the most post-it notes still sticking wins! Start another game by having each team try and shake off all their post-its. The team that shakes off all their post-its without using hands first wins.
Jelly relay: divide players into two teams. Give each team a tablespoon and an empty bowl. At the other end of the room/garden, place a bowl full of jelly. Teams race back and forward to see who can get the most jelly in their bowl within 5 (or 10) minutes.
The good old chocolate game: sit in circle, take turns to roll a dice, if you roll a 6 you put on hat, scarf and gloves and use knife and fork to eat individual chunks from a choc bar on a plate until next person rolls a 6.
Have a treasure hunt around the house and/or garden. For my 8yo DD, we hid hair clips and scrunchies. For my DS, we hid little rubbers.
Who's hidden? Send one player out of room. Choose another child to be hidden under a blanket. Child comes back into room and has 3 guesses to name the child that is under the blanket.
Shoebox shuffle relay: Each team gets 2 shoe boxes. They must race to a cone and back while wearing shoe boxes on their feet. When they return the next person on their team races. They will have to shuffle their feet or they will step out of the boxes. Also if a box is broken that team loses.