This sentence tests the fixed preposition pattern that goes with the verb 'condole'. In standard English you condole with a person, using 'with', and you condole on an event or loss, using 'on'. The underlined part reads: 'to condole for you on'.
Option (d) is correct because 'condole with you on the death' is the accepted idiomatic pairing, unlike the other three options which each get one of the two prepositions wrong.
Let's summarize:
So the corrected sentence reads 'I pen these few lines to condole with you on the death of your beloved mother', matching option (d).
If the price of a commodity increases by 25%, by what percentage should the consumption be reduced to keep the expenditure the same?