This is a case of parallelism. Not only on has to be followed by but also on. Hence A,C and E are out. Between B and D, b wins because of meaning clarity.
The expansion of the Mongol empire depended not only on the Mongols' rigorous training and the discipline of their soldiers but also they implemented a highly organized supply and communication network among their many widespread armies and then enabling them to receive their current orders and some replenishment of their weaponry.
A. they
...
The expansion of the Mongol empire depended not only on the Mongols' rigorous training and the discipline of their soldiers but also they implemented a highly organized supply and communication network among their many widespread armies and then enabling them to receive their current orders and some replenishment of their weaponry.
A. they
...



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