अट्कुप्वाङ्नुम्व्यवायेऽपि

The substitute ण् takes the place of न् , even when a vowel or य् , व् , ह् or a guttural, or a labial, or the preposition आ , or the augment नुम् intervenes, causing separation.
The pratyahara अट् stands for vowels and the letters ह य व र. Thus करणम्, हरणम्, किरिणा, गिरिणा, कुरुणा, गुरुणा &c.

The कु means all the gutturals, e. g. अर्केण, मूर्खेण, गर्गेण, अर्घेण ॥

The पु means all the labials, e. g. दर्पेण, रेफेण, गर्भेण, चर्म्मणा, वर्मणा ॥

The आङ् means the particle आ : e. g. पर्याणद्धम् from नह् 8.2.34 निराणद्धम् (cf 8.4.14. The particle आ is a vowel and so included in अट् pratyahara. Its specification in the sutra shows that the restriction of the rule to the letters occurring in the same word, does not apply in the case of आङ्, in which case the rule applies to letters separated by another word.

So also when the anusvara separates the letters e. g. वृंहणम्, वृंहणीयम् ॥

It is from the root वृहिवृद्धौ, the नुम् is added, because the root is इदित 7.1.58 and न् changed to anusvara by 8.3.24. Question:- Well the intervention is here by Anusvara and not नुम्, why is then नुम् taken in the sutra?

The word नुम् in the sutra refers to anusvara, and must be taken co-extensive with it. Otherwise the rule would not apply to words like तृंहणं from तृंह स्तृंह हिंसार्थे ॥ Here the anusvara is not the substitute of the augment नुम् but an original anusvara. Even where there is an augment नुम्, but where it is not changed into anusvara, the rule does not apply. As प्रेन्वनम्, प्रेन्वनीयम् from इविः प्रीणनार्थः ॥

The rule will apply even when these letters are combined in any possible way, or occur singly. As अर्केण, here a guttural and a vowel i. e. 2 letters come between र and न ॥ See 8.3.58 in the case of ष ॥