jmc

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.