Answer:
8/27 of hydrogen peroxide from the stock bottle
Step-by-step explanation:
• The amount of hydrogen peroxide retrieved by James = 2/3
,
• The amount the pharmacist instructs James to retrieve = 4/9 times 2/3
This gives the expression:

Multiply the numerators and the denominators.

Observe that the result cannot be simplified further.
Thus, James needs 8/27 of hydrogen peroxide from the stock bottle to prepare the bulk compound.