Here are the HP Pavilion P2-1180d specifications:

Pavilion p2-1180d
CPU Intel (R) Core(TM) i3-2120T 2.60GHz
Ram 6 Gb
Chipset: Intel H61
Socket: LGA1155
Bus Speed: DMI 5GT/s

Is that possible to install Mountain Lion 10.8.x or lower version (Leopard/Snow Leopard) to this machine?

listning Iam think its possible just verify if you have ahci sata mode I am think you have
after you need installesd.dmg at google and for create bootable thumd drive you need mac or hackintosh,or virtual box windows
or you try to boot whit dvd iakos niresh or this one
Download OS X 10.8 Mountain Lion bootable DVD for Intel PCs Torrent - KickassTorrents
you need dvd double lever 8,5 gig
and lets go try and if you whant my support and help I AM here
you have good pc i3 6gig of ram grafic hd3000!!!