Radon's electron configuration is [Xe] 6s2 4f14 5d10 6p6. The valence electrons are the ones in the outermost shell, here the sixth: 6s2 and 6p6, or 2 + 6 = 8. The 4f14 and 5d10 electrons belong to inner shells and do not count.
Eight is the same valence count as the other heavy noble gases: krypton's configuration ends in 4s2 4p6 and xenon's in 5s2 5p6. All three sit in the noble gas block, and radon and krypton both have an oxidation state of 0. Radon is essentially inert, though fluorine has been reported to react with it to form a fluoride.
In total, a neutral radon atom has 86 electrons, matching its atomic number of 86; the eight valence electrons are the outermost of those. Drawn as a Lewis dot structure, which shows only valence electrons, radon is the symbol Rn with eight dots around it: the filled 6s2 pair and the three filled pairs of 6p6, with no unpaired electron left to share.
What to do next: see the radon element guide for the full property table, and remember that radon's health effects come from its radioactivity, not its chemistry. Test your home to find its level.