महाभारतः mahābhārataḥ - book-12, chapter-61, verse-2

वानप्रस्थं भैक्षचर्यां गार्हस्थ्यं च महाश्रमम् ।
ब्रह्मचर्याश्रमं प्राहुश्चतुर्थं ब्राह्मणैर्वृतम् ॥२॥

2. vānaprasthaṁ bhaikṣacaryāṁ gārhasthyaṁ ca mahāśramam ,
brahmacaryāśramaṁ prāhuścaturthaṁ brāhmaṇairvṛtam.

2. vānaprastham bhaikṣacaryām gārhasthyam ca mahāśramam
| brahmacaryāśramam prāhuḥ caturtham brāhmaṇaiḥ vṛtam

2. vānaprastham bhaikṣacaryām gārhasthyam ca mahāśramam
prāhuḥ brahmacaryāśramam caturtham brāhmaṇaiḥ vṛtam

2. They declare the forest-dweller (vānaprastha) stage, the mendicant (bhaikṣacaryā) stage, and the householder (gārhasthya) stage, which is considered a great stage of life. The student (brahmacarya) stage is called the fourth, observed by Brahmins.

Words meanings summery:

• वानप्रस्थम् (vānaprastham) - one of the four stages of life (āśramas), where one retires to the forest (the forest-dweller stage, the hermit stage)

• भैक्षचर्याम् (bhaikṣacaryām) - referring to the life of a renunciant (sannyāsa), characterized by begging (the practice of mendicancy, begging for alms, a mendicant's life)

• गार्हस्थ्यम् (gārhasthyam) - one of the four stages of life (āśramas), focusing on family and social duties (the state of a householder, householder stage)

• च (ca) - connects 'gārhasthyam' with the preceding items. (and, also)

• महाश्रमम् (mahāśramam) - referring to the householder stage (gārhasthya) as the great stage (the great stage of life, the great effort/toil)

• ब्रह्मचर्याश्रमम् (brahmacaryāśramam) - one of the four stages of life (āśramas), where one studies and practices celibacy (the student stage of life, the stage of celibacy)

• प्राहुः (prāhuḥ) - (authorities or wise persons) declare or assert (they say, they declare, they state)

• चतुर्थम् (caturtham) - referring to brahmacaryāśrama as the fourth in a list (the fourth)

• ब्राह्मणैः (brāhmaṇaiḥ) - by the learned or priestly class of society (by Brahmins, by those who know Brahman)

• वृतम् (vṛtam) - the brahmacarya āśrama is practiced or upheld by Brahmins (chosen, observed, practiced)

Words meanings and morphology

वानप्रस्थम् (vānaprastham) - one of the four stages of life (āśramas), where one retires to the forest (the forest-dweller stage, the hermit stage)

(noun)

Accusative, masculine, singular of vānaprastha

vānaprastha - forest-dweller, one who has retired to the forest

Compound type : tatpuruṣa (vana+prastha)

• vana – forest, wood
  noun (neuter)
• prastha – going, departing, residing
  noun (masculine)
  derived from pra-sthā (to go forth)
  Prefix: pra
  Root: sthā (class 1)

Note: The form ends in -am here because it's an object.

भैक्षचर्याम् (bhaikṣacaryām) - referring to the life of a renunciant (sannyāsa), characterized by begging (the practice of mendicancy, begging for alms, a mendicant's life)

(noun)

Accusative, feminine, singular of bhaikṣacaryā

bhaikṣacaryā - practice of mendicancy, begging for alms

derived from bhikṣā (alms) + caryā (conduct)

Compound type : tatpuruṣa (bhikṣā+caryā)

• bhikṣā – alms, begging
  noun (feminine)
  Root: bhikṣ (class 1)
• caryā – conduct, practice, course
  noun (feminine)
  derived from car (to move, to practice)
  Root: car (class 1)

गार्हस्थ्यम् (gārhasthyam) - one of the four stages of life (āśramas), focusing on family and social duties (the state of a householder, householder stage)

(noun)

Accusative, neuter, singular of gārhasthya

gārhasthya - householdership, the state of a householder

derived from gṛhastha (householder)

च (ca) - connects 'gārhasthyam' with the preceding items. (and, also)

(indeclinable)

महाश्रमम् (mahāśramam) - referring to the householder stage (gārhasthya) as the great stage (the great stage of life, the great effort/toil)

(noun)

Accusative, masculine, singular of mahāśrama

mahāśrama - great stage of life, great hermitage, great effort

Compound type : karmadhāraya (mahā+āśrama)

• mahā – great, large, mighty
  adjective
• āśrama – stage of life, hermitage, monastery
  noun (masculine)
  Prefix: ā
  Root: śram (class 4)

Note: Accusative singular.

ब्रह्मचर्याश्रमम् (brahmacaryāśramam) - one of the four stages of life (āśramas), where one studies and practices celibacy (the student stage of life, the stage of celibacy)

(noun)

Accusative, masculine, singular of brahmacaryāśrama

brahmacaryāśrama - the student stage, the celibate stage of life

Compound type : tatpuruṣa (brahmacarya+āśrama)

• brahmacarya – religious student, celibacy, holy life
  noun (neuter)
• āśrama – stage of life, hermitage, monastery
  noun (masculine)
  Prefix: ā
  Root: śram (class 4)

प्राहुः (prāhuḥ) - (authorities or wise persons) declare or assert (they say, they declare, they state)

(verb)

3rd person , plural, active, perfect (liṭ) of bru

perfect tense (liṭ)

3rd person plural active (irregular form of brū/vac)

Root: bru (class 2)

Note: Often used impersonally or with implied subject 'they' (wise people).

चतुर्थम् (caturtham) - referring to brahmacaryāśrama as the fourth in a list (the fourth)

(numeral)

Note: Agrees with brahmacaryāśramam in case and number.

ब्राह्मणैः (brāhmaṇaiḥ) - by the learned or priestly class of society (by Brahmins, by those who know Brahman)

(noun)

Instrumental, masculine, plural of brāhmaṇa

brāhmaṇa - Brahmin, a member of the priestly class, one connected with Brahman

derived from brahman (Vedic text, sacred knowledge, ultimate reality)

Note: Agent of the action vṛtam (chosen/observed).

वृतम् (vṛtam) - the brahmacarya āśrama is practiced or upheld by Brahmins (chosen, observed, practiced)

(adjective)

Accusative, masculine, singular of vṛta

vṛta - chosen, selected, observed, surrounded

past passive participle

derived from root vṛ (to choose, to cover)

Root: vṛ (class 5)

Note: Modifies brahmacaryāśramam.