NOTE: 'Sympathy' means feelings of pity and sorrow for someone's misfortune.
Option A - 'Solace' is a noun as well as a verb which means comfort or to give comfort. As we need an adverb to convert 'with sympathy', we can't use 'solace'. Hence, option
A is incorrect.Option B - 'Systematic' is an adjective and hence we can't use it here. Thus option B is incorrect.
Option C - 'Sympathetic' is an adjective, which means being comforting and supportive. Hence, option C is incorrect.
Option D - 'Sympathetically' is an adverb, which means to do something with pity and sorrow. Hence, we can use 'sympathetically' to replace 'with sympathy'. Thus option D is the correct answer.