How to calculate the mass of hydrogen in a borane sample?
The problem does not need any difficult approach, not even relative atomic masses, if you trust the one who made this exercise. Since borane (whatever type it is)* consists (by exercise's hypothesis) only of hydrogen and boron and since boron is $85.63\%$ by mass, hydrogen's mass percentage would be the remaining $100\% - 85.63\% = 14.37\%$. Therefore, we have $\pu{6.60 g}$ of hydrogen in this sample.

The compound borane, $\ce{BH3}$, is about $78.1\%$ boron per mass. However, there is a class of compounds called boranes which also only consist of boron and hydrogen. From this class pentaborane(9), $\ce{B5H9}$, with about $85.7\%$  boron by mass would fit the exercise.