Kind scholars,
Please kindly explain the nature (part of speech) and function of the word ariyaṁ in this sentence.
ariyaṁ vo, bhikkhave, aṭṭhaṅgikaṁ maggaṁ desessāmi vibhajissāmi.
Thank you 
ariyaṃ is the accusative singular of the adjective ariya (noble) describing the magga (path), which is also described by the adjective aṭṭhaṅgika (that which has eight limbs/parts).
The buddha is saying - Hey monks, I’m going to teach and conceptually dissect for you the noble eightfold path.
(Skt: āryaṃ vo bhikṣavo’ṣṭāṅgam mārgaṃ deśayiṣyāmi vibhakṣyāmi)
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Looking at the translations, I thought so too.
However, the word ‘vo’ confounds me a bit. So, I thought whether it is possible that ariyaṁ modifies the pronoun vo.
vo simply means “you” (tvaṃ) in accusative plural (referring to the monks), while ariyaṃ is accusative singular, describing the maggaṃ
An adjective must follow its substantive noun in declension and number, so ariyaṃ should be accusative singular as maggaṃ is accusative singular.
ariyaṃ cannot describe vo which is plural.
Ahhhh I see.
plural, singular…
Thank you so much.
No. It’s dative plural here. “I will explain and analyze for y’all”
Yes. Pāli will often throw words—vocatives, conjunctions, discourse markers, etc—in between an adjective and its substantive. It’s one of the fun quirks of Pāli! 
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You’re right, catutthī does fit the sense better, thanks for the correction.
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