'Lodging and boarding' refers to accommodation. Hence this word means the same as the given expression and option B is correct.
Option A: 'Cafe' is 'a small restaurant selling light meals and drinks'.
Option C: 'Restaurant' means 'a place where people pay to sit and eat meals that are cooked and served over there'.
Option D: 'Motel' is 'a roadside hotel'.
These words do not mean the same as the given expression. Hence options A, C and D are wrong.