• bhagavatā — by the personal expansion of the Supreme Lord (Vyāsadeva)
  Instrumental of bhagavat. Vyāsa is called bhagavat — a partial expansion of Viṣṇu. Gauḍīyas: Vyāsa is enumerated as one of the śaktyāveśa-avatāras (CC Madhya 20.246). He acts with the Lord's empowering presence.
• sabhājitaḥ — honored
  Past participle of sabhāj. Properly received and honored. Gauḍīyas: sabhājana — the welcome-protocol — is a structural feature of paramparā. CC describes Mahāprabhu's hosts performing it for Him at every village.
• nārāyaṇa-mukhāt — from the mouth of Śrī Nārāyaṇa Ṛṣi
  Compound: Nārāyaṇa + mukha (mouth). Hearing from the Lord's own mouth. Gauḍīyas: the highest pramāṇa is bhagavat-mukha-vāk — the Lord's directly-spoken word. Bhāgavatam contains both: directly (Kṛṣṇa to Uddhava, 11.6-29) and via expansions (Nārāyaṇa here).
• varṇayām āsa — he described
  Periphrastic perfect of √varṇ. Description as Vedic act. Gauḍīyas: the verb varṇana underlies the entire Bhāgavata project — Vyāsa is the great varṇayitā, the describer. SB is by structure a sequence of varṇanas.
• śrutam — what he had heard
  Past participle of √śru. The transmitted content. Gauḍīyas: śruta — that which was heard — is the technical name of the Vedic corpus itself. Nārada transmits to Vyāsa his śruta from Nārāyaṇa, and the chain continues.

Vyāsa, himself an avatāra of Viṣṇu, rises to greet Nārada — for the receiver in paramparā honours the bringer, not the other way around. Vyāsa is the future compiler; Nārada is the present courier. The chapter we hold in our hands is the result of this hand-off in the hermitage.