This is the reduction reaction of a tertiary alcohol by sodium, the proposed mechanism is as depicted in the following scheme.
The products of this reaction are: tert-butoxide (#(CH_3)_3C-O^-#), sodium ion (#Na^+#) and elemental hydrogen (#H_2#).
The above scheme shows two possible mechanism for sodium to lose its valence electron to.
The #color(red)(red)# arrows show that sodium gives its valence electron to hydrogen and the hydrogen loses its electron to oxygen to form hydrogen radical and tert-butoxide.
The #color(blue)(blue)# arrows show that sodium gives its valence electron to oxygen and then there is a hemolytic cleavage of the #O-H# bond to form hydrogen radical and tert-butoxide.
Finally, two hydrogen radicals combine together to form #H_2#; the elemental hydrogen.
Note that Sodium is oxidized (from #0# to #+1#) and hydrogen is reduced (from #+1# to #0#).