Option A: The phrase, 'blew up' means 'exploded' or 'caused to explode'. The sentence, 'The angry protesters blew up the track when their demands were not met' means: As their demands were not met, the angry protestors set up bombs (or explosives) and cause to explode the railway tracks'. As it conveys a clear meaning when used in the given sentence, option A is correct.
Option B: The phrase, 'blew over' means 'faded away without serious consequences'. An example of its usage is: All their troubles were blown over when they won the lottery.
Option C: The phrase, 'blew in' means 'arrived casually and without notice'. An example of its usage is:A strong wind blew in and knocked off our curtains.
Option D: The phrase, 'blew through' means 'moved or carried by wind or air'. An example of its usage is:A strong wind blew in through the door.
Given the meanings as above, the phrases given in options B, C and D cannot be used in the blank to form a meaningful sentence. Hence, these options are incorrect.