The ratio of two supplementary angles is 6: 3. what is the measure of the smaller angle?

So 6:3 
simplify 
2:1
That means that the bigger angle is two times bigger than the smaller one
supplementary angles equal up to 180

smaller angle + larger angle = 180
s + l = 180
we can create our second equation using two times the smaller = larger
2s = l
our two equations are:
2s = l
s + l = 180
now that we have  the two equations, we can solve using substitution to isolate the variable.
s + l = 180
s + (2s) = 180
simplify.
3s = 180
s = 60
the smaller angle has a value of 60.
now, remember that the larger angle is two times the smaller.
60 x 2 = 120
smaller angle: 60
larger angle: 120
we know this is correct because we know the smaller is 1/2 or 1:2 or 2:4 times the bigger, and the two angles add up to be 180      (60 + 120)

Hope this helps :)