Parimukhaṃ is used in the context of ānāpānasati. It is found in the phrase 'parimukhaṃ satiṃ upaṭṭhapetvā', and is a compound with pari (around) and mukha (mouth, entrance). According to the dictionary pari also means '(lit.) away from, off' and mukha 'face, entrance, front, top'.
Ānāpānasati is a compound of ānāpāna and sati. Sati is meditation (see Sati) and ānāpāna is about the breathe not breath if that distinction helps. Meditation is something we need to develop and here we hone this on the breathe.
We are told to be meditative on the breathe knowing whether it is in or out and f.i. long or short. Whilst knowing so we thus train with f.i. body, feeling, mind and principles (SN54.1, SN54.13). Parimukhaṃ describes this way of attending (upaṭṭhapetvā). We can describe it as 'away from the front', 'around the front' to indicate what is at the centre of our attention and what at the side. Or at the foreground and background. What we fathom and train gets to be the centre of our attention, the foreground, and the meditative breathe in or breathe out then surrounds that, as the context or background. This manner then is covered by the word peripheral, with peripherally (parimukhaṃ) being the adverb.
Parimukhaṃ (adv.) peripherally.