The sides of triangle are 3 consecutive even integers with the largest side being less than 13. What is the total number of such triangles?

We have 4 cases 
1: Largest side = 12  then Sides of the triangle are 8,10,12
2: Largest side = 10  then Sides of the triangle are 10,8,6
3: Largest side = 8  then Sides of the triangle are 8,6,4
4: Largest side = 6  then Sides of the triangle are 6,4,2
According to the properties of the triangle,
Sum of any two sides of a triangle is greater than the third side and difference of any two sides of a triangle is lesser than the third side
All the above cases satisfy the properties of the triangle except case 4 
Hence C is the correct answer.