Achemical engineer has determined by measurements that there are 0.040 moles of carbon in a sample of methyl tert-butyl ether. how many moles of oxygen are in the sample?

0.008 moles

First, you need to determine the chemical formula of methyl tert-butyl which is (CH3)₃COCH₃. From there you need to figure out how many carbon atoms there are per molecule and how many oxygen atoms there are per molecule.
The CH₃ section has 1 carbon atom. That section is duplicated 3 times for a total of 3 carbon atoms. The trailing section of COCH₃ has another 2 carbon atoms so you have a total of 5 carbon atoms per molecule. And the COCH3 section has only 1 oxygen atom, giving a total of 1 oxygen atom per molecule of Methyl tert-butyl. So now you know there's 5 carbon atoms per oxygen atom, so the number of moles of Oxygen is one fifth the number of moles of carbon.

Moles Oxygen = Moles Carbon / 5
Moles Oxygen = 0.040 / 5
Moles Oxygen = 0.008