BhG 4.20

syntax

[yaḥ] (he who) karma-phalāsaṅgam (attachment to the fruit of activities) tyaktvā (after abandoning),
nitya-tṛptaḥ (ever satisfied) nirāśrayaḥ (without shelter) [san] (being),
saḥ (he) karmaṇi (in activity) abhipravṛttaḥ api (although engaged) kiṁ-cit eva (indeed nothing) na karoti (he does not do).

grammar

tyaktvā	–	√tyaj (to abandon, to give up) absol. – after abandoning;
karma-phalāsaṅgam	–	karma-phala-āsaṅga 2n.1 m.; TP: karmaṇāṁ phale āsaṅgam iti – attachment to the fruit of activities (from: √kṛ – to do, karman – activity and its result; √phal – to ripen; phala – fruit, result; ā-√sañj – to attach, to stick, to embrace, ā-saṅga – clinging, connection, attachment);
nitya-tṛptaḥ	–	nitya-tṛpta 1n.1 m.; nityaṁ tṛpta iti – ever satisfied (from: av. nityam – constantly, eternally; √tṛp – to be satisfied, PP tṛpta – satisfied);
nirāśrayaḥ	–	nir-ā-śraya 1n.1 m. – without shelter (from: niḥ – out of, away from, without; ā-√śri – to lean on, to rest on, to depend on, āśraya – place of refuge, shelter);
karmaṇi	–	karman 7n.1 n. – in activity (from: √kṛ – to do);
abhipravṛttaḥ	–	abhi-pra-vṛtta (pra-√vṛt – to start to act, to surpass) PP 1n.1 m. – advancing, proceding, engaged;
api	–	av. – although, moreover, besides, even;
na	–	av. – not;
eva	–	av. – certainly, just, merely;
kiṁ-cit	–	kiṁ-cit sn. 2n.1 m. – something (from: kim – what?; -cit – indefinitive particle);
karoti	–	√kṛ (to do) Praes. P 1v.1 – he does;
saḥ	–	tat sn. 1n.1 m. – he;

textual variants

nirāśrayaḥ → nirāmayaḥ (with no sickness);
karmaṇy abhipravṛtto ‚pi → karmaṇy api pravṛtto ‚pi / karmabhiḥ sampravṛtto ‚pi (although in activity engaged / even engaged in activities);
saḥ → me (for me / my);

The fourth pada of verse 4.20 is the same as the first pada of verse BhG 5.8;

Śāṃkara

yas tu karmādāv akarmādi-darśī so’karmādi-darśanād eva niṣkarmā sannyāsī jīvana-mātrārtha-ceṣṭaḥ san karmaṇi na pravartate, yadyapi prāg-vivekataḥ pravṛttaḥ | yas tu prārabdha-karmā sann uttara-kālam utpannātma-samyag-darśanaḥ syāt, sa sarva-karmaṇi prayojanam apaśyan sa-sādhanaṃ karma pariyajaty eva | sa kutaścin nimittāt karma-parityāgāsambhave sati karmaṇi tat-phale ca saṅga-rahitatayā sva-prayojanābhāvāl loka-saṅgrahārthaṃ pūrvavat karmaṇi pravṛtto’pi naiva kiṃcit karoti jñānāgni-dagdha-karmatvāt tadīyaṃ karmākarmaiva sampadyata ity etam arthaṃ darśayiṣyann āha

tyaktvā karmasv abhimānaṃ phalāsaṅgaṃ ca yathoktena jñānena nitya-tṛpto nirākāṅkṣo viṣayeṣv ity arthaḥ | nirāśraya āśraya-rahitaḥ | āśrayo nāma yad āśritya puruṣārthaṃ sisādhayiṣati | dṛṣṭādṛṣṭa-phala-sādhanāśraya-rahita ity arthaḥ | viduṣā kriyamāṇaṃ karma paramārthato’karmaiva | tasya niṣkriyātma-darśana-sampannatvāt | tenaivambhūtena sva-prayojanābhāvāt sa-sādhanaṃ karma parityaktavyam eveti prāpte, tato nirgamāsambhavāl loka-saṅgraha-cikīrṣayā śiṣṭa-vigarhaṇāparijihīrṣayā vā pūrvavat karmaṇy-abhipravṛtto’pi niṣkryātma-darśana-sampannatvān naiva kiṃcit karoti saḥ

Rāmānuja

etad eva vivṛṇoti

karmaphalasaṅgaṃ tyaktvā nityatṛptaḥ nitye svātmny eva tṛptaḥ, nirāśrayaḥ asthiraprakṛtau āśrayabuddhirahito yaḥ karmāṇi karoti, sa karmaṇy ābhimukhyena pravṛtto ‚pi naiva kiṃcit karma karoti karmāpadeśena jñānābhyāsam eva karotītyarthaḥ

Śrīdhara

kiṃ ca tyaktveti | karmaṇi tat-phale cāsaktiṃ tyaktvā nityena nijānandena tṛptaḥ | ataeva yoga-kṣemārtham āśrayaṇīya-rahitaḥ | evambhūto yaḥ svābhāvike vihite vā karmaṇy abhitaḥ pravṛtto ‚pi kiṃcid eva naiva karoti | tasya karmākarmatām āpadyata ity arthaḥ

Madhusūdana

bhavatu jñānāgninā prāktanānām aprārabdha-karmaṇāṃ dāha āgāmināṃ cānutpattiḥ | jñānotpatti-kāle kriyamāṇaṃ tu pūrvottarayor anantar-bhāvāt phalāya bhaved iti bhavet kasyacid āśaṅkā tām apanudaty āha tyaktveti | karmaṇi phale cāsaṅgaṃ kartṛtvābhimānaṃ bhogābhilāṣaṃ ca tyaktvākartr-abhoktr-ātma-samyag-darśanena bādhitvā nitya-tṛptaḥ paramānanda-svarūpa-lābhena sarvatra nirākāṅkṣaḥ | nirāśraya āśrayo dehendriyādir advaita-darśanena nirgato yasmāt sa nirāśrayo dehendriyādy-abhimāna-śūnyaḥ | phala-kāmanāyāḥ kartṛtvābhimānasya ca nivṛttau hetu-garbhaṃ krameṇa viśeṣaṇa-dvayam | evambhūto jīvanmukto vyutthāna-daśāyāṃ karmaṇi vaidike laukike vābhipravṛtto ‚pi prārabdha-karma-vaśāl loka-dṛṣṭyābhitaḥ sāṅgopāṅgānuṣṭhānāya pravṛtto ‚pi sva-dṛṣṭyā naiva kiṃcit karoti sa niṣkriyātma-darśanena bādhitatvād ity arthaḥ

Viśvanātha

nitya-tṛpto nityaṃ nijānandaena tṛptaḥ | nirāśrayaḥ svayoga-kṣemārthaṃ na kam apy āśrayate

Baladeva

uktam arthaṃ viśadayati tyaktveti | karma-phale saṅgaṃ tyaktvā nityenātmanānubhūtena tṛpto nirāśrayo yoga-kṣemaārtahm apy āśraya-rahita īdṛśo yo ‚dhikārī sa karmaṇy abhitaḥ pravṛtto ‚pi naiva kiṃcit karoti | karmānuṣṭhānāpadeśena jñāna-niṣṭhām eva sampādayatīty ārurukṣor daśeyam | etena vikarmaṇaḥ svarūpaṃ bandhakatvaṃ boddhavyam ity uktaṃ bhavati