A pretty confusing question with weird wording:

If the concentration of a compound is 10mg/ml, and its molecular weight is 267.24, how would you make 10 ml, with the compound at 10 µM?

2 answers

The concentration is .010g/ml=10g/l=10/267.24 M=.0374M

so you want to dilute it .0374M/10e-6M... = 3750 times
that means one part original, and 3749 parts water.

so in 10 ml, one part=.01/3740=2.67e-6 liters or 2.67e-3 ml of stock, add solvent (water?) to 10 ml
well, we need how many mols?
we need
10 *10^-6 mols/liter
we need 10^-2 liters of that concentration
so we need 10^-8 mols of compund

we have 10 grams/liter
10 grams/liter / 267 g/mol = .0375 mols/liter
10^-8 mols/ .0375 mols/liter = 26.7 *10^-8 liters = 0.267 µM