The correct answer is Option A.
TAKE OVER means to assume control of something, especially the buying of one company by another.
In the given sentence, the speaker's company is being bought by an American company.
The remaining options are incorrect because:
Option B: BOUGHT means only buying, not assuming control. In the given sentence, the American company will assume control of the speaker's company. Secondly, it cannot be used with 'over'.
Option C: SOLD means to sell.
Option D; RUN means move at a faster speed than walking. The phrasal verb 'run over' means to crush something.
Thus Option A is the correct answer.