योगवासिष्ठः yogavāsiṣṭhaḥ - book-7, chapter-110, verse-32

पटनद्धपताकौघजातसंचारिदोर्द्रुमम् ।
रक्तोज्ज्वलत्वात्त्रैलोक्यलक्ष्म्या भूषणविद्रुमम् ॥ ३२ ॥

paṭanaddhapatākaughajātasaṃcāridordrumam ,
raktojjvalatvāttrailokyalakṣmyā bhūṣaṇavidrumam 32

32. paṭanaddhapatākāoghajātasaṃcāridor-drumam
raktojjvalatvāt trailokyalakṣmyā bhūṣaṇavidrumam

32. paṭanaddhapatākāoghajātasaṃcāridor-drumam
raktojjvalatvāt trailokyalakṣmyā bhūṣaṇavidrumam

32. Whose arm-like trees sway due to the multitude of fastened banners, and which, because of its radiant redness, is like a coral ornament for the prosperity (lakṣmī) of the three worlds.

Words meanings summery:

• पटनद्धपताकाओघजातसंचारिदोर्-द्रुमम् (paṭanaddhapatākāoghajātasaṁcāridor-drumam) - having arm-like trees that move with a multitude of fastened banners

• रक्तोज्ज्वलत्वात् (raktojjvalatvāt) - due to red brilliance; because of shining redness

• त्रैलोक्यलक्ष्म्या (trailokyalakṣmyā) - by the prosperity of the three worlds; for the Lakshmi of the three worlds

• भूषणविद्रुमम् (bhūṣaṇavidrumam) - a coral ornament

Words meanings and morphology

पटनद्धपताकाओघजातसंचारिदोर्-द्रुमम् (paṭanaddhapatākāoghajātasaṁcāridor-drumam) - having arm-like trees that move with a multitude of fastened banners

(adjective)

Accusative, neuter, singular of paṭanaddhapatākāoghajātasaṃcāridor-druma

paṭanaddhapatākāoghajātasaṁcāridor-druma - having arm-like trees that move due to a multitude of fastened banners

Compound type : bahuvrīhi (paṭa+naddha+patākā+ogha+jāta+saṃcārin+doḥ+druma)

• paṭa – cloth; banner
  noun (masculine)
• naddha – tied; fastened; bound
  adjective (masculine)
  Past Passive Participle
  From root √nah (to tie, bind) + -ta suffix
  Root: nah (class 4)
• patākā – banner; flag; standard
  noun (feminine)
• ogha – multitude; flood; stream; heap
  noun (masculine)
• jāta – born; produced; arisen; happened; become
  adjective (masculine)
  Past Passive Participle
  From root √jan (to be born, produced) + -ta suffix
  Root: jan (class 4)
• saṃcārin – moving; roaming; swaying; causing to move
  adjective (masculine)
  From saṃ-√car (to move, wander) + -in suffix
  Prefix: sam
  Root: car (class 1)
• doḥ – arm; hand
  noun (feminine)
• druma – tree; wood
  noun (masculine)

Note: This entire compound acts as an adjective describing something in the accusative case.

रक्तोज्ज्वलत्वात् (raktojjvalatvāt) - due to red brilliance; because of shining redness

(noun)

Ablative, neuter, singular of raktojjvalatva

raktojjvalatva - red brilliance; state of being radiantly red

Compound of 'rakta' (red) and 'ujjvalatva' (brilliance). Suffixed with -tva to form an abstract noun.

Compound type : tatpuruṣa (rakta+ujjvalatva)

• rakta – red; colored; dyed; attached; fond of
  adjective (masculine)
  Past Passive Participle
  From root √rañj (to color, dye) + -ta suffix
  Root: rañj (class 1)
• ujjvalatva – brilliance; splendor; shining state
  noun (neuter)
  Derived from 'ujjvala' (brilliant) with the suffix -tva
  Prefix: ut
  Root: jval (class 1)

Note: Functions as an adverbial phrase meaning 'due to'.

त्रैलोक्यलक्ष्म्या (trailokyalakṣmyā) - by the prosperity of the three worlds; for the Lakshmi of the three worlds

(noun)

Instrumental, feminine, singular of trailokyalakṣmī

trailokyalakṣmī - the prosperity (lakṣmī) of the three worlds; the goddess Lakṣmī of the three worlds

Tatpuruṣa compound of 'trailokya' (three worlds) and 'lakṣmī' (prosperity/goddess Lakṣmī).

Compound type : tatpuruṣa (trailokya+lakṣmī)

• trailokya – the three worlds (heaven, earth, and netherworld)
  noun (neuter)
  From 'tri-loka' (three worlds) + 'ya' suffix for 'relating to'.
• lakṣmī – prosperity; wealth; fortune; beauty; the goddess Lakṣmī
  noun (feminine)

Note: Could also be dative/genitive singular based on context, but instrumental 'by' or 'for the purpose of' seems most fitting here.

भूषणविद्रुमम् (bhūṣaṇavidrumam) - a coral ornament

(noun)

Accusative, neuter, singular of bhūṣaṇavidruma

bhūṣaṇavidruma - a coral ornament; an ornament made of coral

Tatpuruṣa compound of 'bhūṣaṇa' (ornament) and 'vidruma' (coral).

Compound type : tatpuruṣa (bhūṣaṇa+vidruma)

• bhūṣaṇa – ornament; decoration; embellishment
  noun (neuter)
  From root √bhūṣ (to adorn, decorate) + -ana suffix
  Root: bhūṣ (class 10)
• vidruma – coral
  noun (masculine)