"The product of one-third w and eight-ninths" translates to the following:
(1/3)w*(8/9)
which will multiply out to be
(1/3)*(8/9)*w
((1*8)/(3*9))*w
(8/27)*w
Now take one-sixteenth (1/16) of this to get
(1/16)*(8/27)*w
((1*8)/(16*27))*w
(8/432)*w
(1/54)*w
Finally we take 10 less than this expression to get
(1/54)*w - 10
which is very close to what choice C is saying. The only difference is the letter 'u' thrown in. I'm assuming the 'u' was cut off somehow or that there's a typo.
In any event, the most likely answer is choice C.