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. While sati is memory (mindfulness would be sampajañña see SN26.7) it is a bit unfit for the usage in English where recollection fits better. And ānāpāna is about the breathe not breath if that distinction helps. Recollection is something we need to develop and here we hone this on the breathe.
We are told to recollect on the breathe knowing whether it is in or out, and long or short. And whilst knowing this train with body, feeling, mind and principles (SN54.1). 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 train gets to be the centre of our attention, the foreground, and the knowing of the breathe as in or out, and long or short, then surrounds that as the context or background. This manner is thus covered by the word peripheral, with peripherally (parimukhaṃ) being the adverb.
Parimukhaṃ (adv.) peripherally.