How many carbons in this skeletal structure?
Your intuition is not wrong.

There are indeed 6 carbon atoms in the molecule (3-methyl-pentane).

With bondline/skeletal notation, there's a carbon atom at all the vertices; at the ends, and every time the line changes direction.

Counting the carbon atoms then becomes as simple as counting the vertices. 

This becomes more apparent if you explicitly write all the atoms like illustrated below: