When propagating a Begonia (and most other plants) it is best to use a tip cutting, one that has no more than 4 leaves and a bare stem of about 3 inches below the lowest leaf. Long stems are older and don't root as readily and they never lose their legginess. Yours is also in a pot that is way too big.

I suggest taking a tip cutting as I suggested and rooting it in plain water or a very small pot filled with a porous peat-based potting mix