Can I use the recovery disc for my computer, an Advent Quad core, on another computer, a lap top?

It may work but it may not - the recovery disc will have all the extra device drivers for the hardware in the relevant computer but may not have all the drivers for the laptop. In particular, the recovery disc may not see any hard drives on the laptop if they are of different type. If it doesn't, you will need to contact the laptop vendor website - maybe they have a download of the recovery disc.