To start, we can make three equilateral triangles, with sides $ 2,2,2 $, $ 4,4,4 $ and $ 6,6,6 $. Next, look at isosceles triangles. If two sides have length 6, the remaining side could be $ 2 $ since $ 6+2>6 $ and $ 6+6>2 $. The remaining side could also be 4 since $ 6+4>6 $ and $ 6+6>4 $. So, this is two more triangles. If two sides have length 4, the remaining side could have length $ 6 $ since $ 6+4>4 $ and $ 4+4>6 $. The remaining side could also have length 2 since $ 2+4>4 $ and $ 4+4>2 $. There are no possible triangles with all sides of different length, since $ 2+4=6 $. Thus, there are a total of $ \boxed{7} $ non congruent triangles.