We would apply the traingle inequality theorem which states that the sum of the length of two sides of a triangle is greater than the length of the third side. Thus,
For the first option
12 + 10 = 22 and it is less than 23. It can't form the length of the three sides of a triangle
For the second option
6.2 + 6.2 = 12.4 and it is less than 15. It can't form the length of the three sides of a triangle
For the third option,
4.6 + 3.8 = 8.4 and it is greater than 8.2. It can form the length of the three sides of a triangle
For the fourth option
5 + 7 = 12 and it is equal to 12. It can't form the length of the three sides of a triangle
Thus, the correct option is 4.6, 8.2, 3.8