I translate it as "extinguish."
“Dukkhadomanassānaṃ atthaṅgamāya,” means to extinguish pain and sorrow. Here, dukkha means simply physical pain, while domanassa is mental pain or sorrow. The expression “Suriye atthaṅgama,” means the setting of the sun. In hot countries like Bihar where the Buddha mostly taught, the sun is extremely hot and oppressive from early morning to late evening. When it finally falls down to the horizon and sets, the burning finally ceases. Physical pain is extremely oppressive, and when it ceases, one feels great relief. The mental pain of sorrow, too, is very difficult to bear. The mind feels heavy and unresponsive. Although one wishes only to be happy, sad thoughts pervade the mind and if dwelt upon, only lead to greater despair. When sorrow is replaced by happiness, the mind is again buoyant and optimistic.
The PTS Dictionary says this:
ttha2 (p. 24) (nt.) [Vedic asta, of uncertain etym.] home, primarily as place of rest & shelter, but in P. phraseology abstracted from the "going home", i. e. setting of the sun, as disappearance, going out of existence, annihilation, extinction. Only in acc. and as °- in foll phrases: atthangacchati to disappear, to go out of existence, to vanish Dh 226 (= vināsaṃ natthibhāvaṃ gacchati DhA III.324), 384 (= parikkhayaṃ gacchati); pp. atthangata gone home, gone to rest, gone, disappeared; of the sun (= set): J I.175 (atthangate suriye at sunset); PvA 55 (id.) 216 (anatthangate s. before sunset) fig. Sn 472 (atthagata). 475 (id.); 1075 (= niruddha ucchinṇa vinaṭṭha anupādi-sesāya nibbāna-dhātuyā nibbuta); It 58; Dhs 1038; Vbh 195. -atthagatatta (nt. abstr.) disappearance SnA 409. -atthangama (atthagama passim) annihilation, disappearance; opposed to samudaya (coming into existence) and synonymous with nirodha (destruction) D I.34, 37, 183; S IV.327; A III.326; Ps II.4, 6, 39; Pug 52; Dhs 165, 265, 501, 579; Vbh 105. -atthagamana (nt.) setting (of the sun) J I.101 (suriyass' atthagamanā at sunset) DA I.95 (= ogamana). - attha-gāmin, in phrase udayɔ atthagāmin leading to birth and death (of paññā): see udaya. -atthaṃ paleti = atthangacchati (fig.) Sn 1074 (= atthangameti nirujjhati Nd2 28). - Also atthamita (pp. of i) set (of the sun) in phrase anatthamite suriye before sunset (with anatthangamite as v. l. at both pass.) DhA I.86; III.127. - Cp. also abbhattha.
