A horizontal compression is given by the following transformation rule:
g(x) = f(bx)
Where the graph of g(x) will be the result of compressing f(x) horizontally by a factor of b.
A downward shift of "a" units is given by the following transformation rule:
g(x) = f(x) - a
Where the graph of g(x) results when we translate "a" units down the graph of f(x).
As you can see, in order to get a horizontal compression we have to multiply the variable x by a compression factor, in this case, 3. on the other hand we have to translate the function 15 units down, then we have to subtract 15. From the given options only option B met these characteristics, then option B is the correct answer.