I guess there is a typo . See red.
This is just a very basic application of the sine rule and it's very obvious . Just draw a triangle and you should be able to see.
8/ sin 40 = 6/sin B
Then the sum of angles of a triangle will tell you angle C .
so now use the sine rule once again .
8/sin 40 = c/ sin C
OR you can use the cosine rule , its faster .
8^2=6^2+c^2-2(6)(c)cos 40 .
solve for c .