Unemployment was on the increase during the end of the carter term, and continued into the Reagan administration. The numbers are right on the bureau of labor statistics site. The 10.8% figure for November and December 1982 is correct. However, the 1.9% increase between Jan-june of this year is the highest rate of climb since 1948. It is widely acknowledged that the early 80’s recession was sparked by the Iranian revolution in 1979 and the 79 energy crisis. Carters mishandling of the Iranian hostage crisis only made things worse.
Not sure why you mention Bush2, but unemployment during his administration was actually pretty low.