"He needs to get it fixed else he'll face a lot of trouble soon", I told him.

The tense of the sentence inside the inverted commas [reported speech] is Simple Present, and the tense of the reporting verb is past. This means that when converting to indirect, the reported speech will become past simple. Hence, the correct conversion will be: "I told him that he needed to get it fixed or he would face a lot of trouble soon ", which is option B. 

[ 'he'll' means 'he will', which becomes 'he would' in the change ]