Every 1/2 hour naomi stretches her neck; every 1/3 hour she stretches her legs; and every 1/6 hour she stretches her arms. which parts of her body will naomi stretch when 2/3 of an hour has passed?

1/2 = 30 mins
1/3 = 20 mins
1/6 = 10 mins

2/3 = 40 mins

Now identify the times that are factors of 40
1, 40
2, 20
4, 10
5, 8

10 and 20 are the only corresponding times, therefore she will stretch her legs and arms after 2/3 of an hour has passed.

every 1/2 hour = 30 mins = stretches her neck
every 1/3 hour = 20 mins = stretches her legs
every 1/6 hour = 10 mins = stretches her arms

2/3 hour = 40 mins.

Naomi will stretches her legs and her arms at 40 mins of an hour.

In an hour, Naomi will stretch her neck two times, stretch her legs three times, and stretch her arms six times.