If A is a subset of B, then all elements from a set A are in a set B.
The number 8 from {3, 8, 6} is not in the set {1, 2, 3, 4, 5, 6}. Therefore {3, 8, 6} is not a subset of {1, 2, 3, 4, 5, 6}.
[tex]\{3,\ 8,\ 6\}\not\subset\{1,\ 2,\ 3,\ 4,\ 5,\ 6\}[/tex]