this is a perfect question for PLUGGING IN THE ANSWER CHOICES and WORKING BACKWARDS.

first, realize that the RATES for these pipes, as usual, are the RECIPROCALS of the given times for 1 tank.
this is so because the rate units are tanks per hour, although you should simply memorize the fact that rates are reciprocals of the time taken to perform 1 job.

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as is customary for "working backwards", you should start with the middle choice, (c).
this means 4 inlet pipes, each of whose rate is +1/8 tank per hour (per the problem statement), for a total inlet rate of +4/8, or +1/2.
also, this means 4 outlet pipes, each of whose rate is -1/6 tank per hour (per the problem statement), for a total outlet rate of -4/6, or -2/3.

therefore, the total rate for choice (c) is +1/2 - 2/3, or -1/6.
this is exactly the overall rate demanded in the problem, so, choice (c) wins.

had this NOT been the correct answer, we'd look at the result, and, based on whether the overall rate was too big or too small, we'd eliminate either a/b/c or c/d/e.