BhG 3.40

syntax

indriyāṇi (the senses), manaḥ (the mind), buddhiḥ (intelligence) asya (its) adhiṣṭhānam (seat) ucyate (it is said).
eṣaḥ (this) etaiḥ (by these) jñānam (knowledge) āvṛtya (after covering)
dehinam (the embodied) vimohayati (it bewilders).

grammar

indriyāṇi	–	indriya 1n.3 n. – the senses (from: √ind – to be powerful);
manaḥ	–	manas 1n.1 n. – the mind (from: √man – to think);
buddhiḥ	–	buddhi 1n.1 f. – intelligence, thought, understanding, knowledge, idea, opinion (from: √budh – to wake, to perceive, to understand);
asya	–	idam sn. 6n.1 n. – its;
adhiṣṭhānam	–	adhiṣṭhāna 1n.1 n. – base, position, abode, seat (from: adhi-√sthā – to stand upon, to superintend);
ucyate	–	√vac (to speak) Praes. pass. 1v.1 – it is said;
etaiḥ	–	etat sn. 3n.3 m. – by these;
vimohayati	–	vi-√muh (to become confused, bewildered, stupefied) Praes. caus. P 1v.3 – it bewilders;
eṣaḥ	–	etat sn. 1n.1 m. – this;
jñānam	–	jñāna 2n.1 n. – knowledge, wisdom, intelligence (from: √jñā – to know, to understand);
āvṛtya	–	ā-√vṛ (to cover) absol. – after covering;
dehinam	–	dehin 2n.1 m. – the embodied one (from: √dih – to anoint, to smear, deha – a form, shape, body; dehin = dehavant = dehābhimānin – who possesses a body, thinking about oneself as a body);

textual variants

vimohayaty eṣa → vimohayaty eṣu (it bewilders, in them);
dehinam → dehināṁ / dehinaḥ (of the embodied, the embodied);

Śāṃkara

The key:
an excerpt from the commented verse
quotes from the scriptures
starting polemic

The seat of desire. He now tells us where is seated desire which, by enveloping wisdom, forms the enemy of the whole world. The seat of the enemy being known, it is easy to kill it.		kim adhiṣṭhānaḥ punaḥ kāmo jñānasyāvaraṇatvena vairī sarvasya lokasya? ity apekṣāyām āha, jñāte hi śatror adhiṣṭhāne sukhena nibarhaṇaṃ kartuṃ śakyata iti —
The senses, mind, and reason air said to be its seat; veiling wisdom through these, it deludes the embodied.		indriyāṇi mano buddhir asyādhiṣṭhānam ucyate | etair vimohayaty eṣa jñānam āvṛtya dehinam ||3.40||
Its seat: the seat of desire. These: the senses, mind (manas), and reason (buddhi).		indriyāṇi mano buddhiś cāsya kāmasyādhiṣṭhānam āśraya ucyate | etair indriyādibhir āśrayair vimohayati vividhaṃ mohayaty eṣa kāmo jñānam āvṛtya ācchādya dehinaṃ śarīriṇam ||3.40||

Rāmānuja

kair upakaraṇair ayaṃ kāma ātmānam adhiṣṭhitīty atrāha

adhitiṣṭhaty ebhir ayaṃ kāma ātmānam itīndriyāṇi mano buddhir asyādhiṣṭhānam; etair indriyamanobuddhibhiḥ kāmo ‚dhiṣṭhānabhūtair viṣayapravaṇair dehinaṃ prakṛtisaṃsṛṣṭaṃ jñānam āvṛtya vimohayati vividhaṃ mohayati, ātmajñānavimukhaṃ viṣayānubhavaparaṃ karotītyarthaḥ

Śrīdhara

idānīṃ tasyādhiṣṭhānaṃ kathayan jayopāyam āha indriyāṇīti dvābhyām | viṣaya-darśana-śravaṇādibhiḥ saṃkalpenādhyavasāyena ca kāmasya āvirbhāvād indriyāṇi ca manaś ca buddhiś cāsyādhiṣṭhānam ucyate | etair indriyādibhir darśanādi-vyāpāravadbhir āśraya-bhūtair viveka-jñānam āvṛtya dehinaṃ vimohayati

Madhusūdana

jñāte hi śatror adhiṣṭhāne sukhena sa jetuṃ śakyata iti tad-adhiṣṭhānam āha indriyāṇīti | indriyāṇi śabda-sparśa-rūpa-rasa-gandha-grāhakāṇi śrotrādīni vacanādāna-gamana-visargānanda-janakāni vāg-ādīni ca | manaḥ saṅkalpātmakaṃ buddhir adhyavasāyātmikā ca | asya kāmasyādhiṣṭhānam āśraya ucyate | yata etair indriyādibhiḥ sva-sva-vyāpāravadbhir āśrayair vimohayati vividhaṃ mohayati eṣa kāmo jñānam viveka-jñānam āvṛtyācchādya dehinaṃ dehābhimāninam

Viśvanātha

kvāsau tiṣṭhaty ata āha indriyāṇīti | asya vairiṇaḥ kāmasyādhiṣṭhānaṃ mahā-durga-rājadhānyaḥ | śabdādayo viṣayās tu tasya rājño deśā iti bhāvaḥ | etair indriyādibhir dehinaṃ jīvam

Baladeva

vairiṇaḥ kāmasya durgeṣu nirjiteṣu tasya jayaḥ sukara iti tāny āha indriyāṇīti | viṣaya-śravaṇādinā saṅkalpenādhyavasāyena ca kāmasyābhivyakteḥ śrotrādīni ca manaś ca buddhiś ca tasyādhiṣṭhānaṃ mahā-durga-rājadhānī-rūpaṃ bhavati viṣayās tu tasya tasya janapadā bodhyāḥ | etair viṣaya-saṃcāribhir indriyādibhir dehinaṃ prakṛti-sṛṣṭa-dehavantaṃ jīvam ātma-jñānodyatam eṣa kāmo vimohayati ātma-jñāna-vimukhaṃ viṣaya-rasa-pravaṇaṃ ca karotīty arthaḥ