With a triangle, the sum of any two side lengths must be greater than the third side length. If this is not true, then the side lengths cannot make a triangle. Let's go through each set of side lengths and determine which would and wouldn't work.
a. 3, 4, 8 - will not make a triangle
3 + 4 = 7 > 8 = false
3 + 8 = 11 > 4 = true
4 + 8 = 12 > 3 = true
b. 7, 6, 12 - will make a triangle
7 + 6 = 13 > 12 = true
7 + 12 = 19 > 6 = true
6 + 12 = 18 > 7 = true
c. 5, 11, 13 - will make a triangle
5 + 11 = 16 > 13 = true
5 + 13 = 18 > 11 = true
11 + 13 = 24 > 5 = true
d. 4, 6, 12 - will not make a triangle
4 + 6 = 10 > 12 = false
4 + 12 = 16 > 6 = true
6 + 12 = 18 > 4 = true
e. 4, 6, 10 - will not make a triangle
4 + 6 = 10 > 10 = false
4 + 10 = 14 > 6 = true
6 + 10 = 16 > 4 = true
Hope this helps!