For three numbers to represent lengths of the sides of a triangle, the sum of
each pair must be greater than the remaining side

Try a:

(3,3,4)

Adding the 1st and 2nd, we get 3+3 = 6 and that is greater than the 3rd side 4.
Adding the 1st and 3rd, we get 3+4 = 7 and that is greater than the 2nd side 3.
Adding the 2nd and 3rd, we get 3+4 = 7 and that is greater than the 1st side 3.
Therefore (3,3,4) can represent the sides of a triangle.

Try b:

(4,3,6)

Adding the 1st and 2nd, we get 4+3 = 7 and that is greater than the 3rd side 6.
Adding the 1st and 3rd, we get 4+6 = 10 and that is greater than the 2nd side 3.
Adding the 2nd and 3rd, we get 3+6 = 9 and that is greater than the 1st side 4. 
Therefore (4,3,6) can represent the sides of a triangle.

Try c:

(7,7,7)

Adding the 1st and 2nd, we get 7+7 = 14 and that is greater than the 3rd side 7.
Adding the 1st and 3rd, we get 7+7 = 14 and that is greater than the 2nd side 7.
Adding the 2nd and 3rd, we get 7+7 = 14 and that is greater than the 1st side 7.
Therefore (7,7,7) can represent the sides of a triangle.

Try d:

(3,6,9)

Adding the 1st and 2nd, we get 3+6 = 9. Oh oh! that is greater than the 3rd
side 9.

So (3,6,9) cannot represent the lengths of the sides of a triangle.

Even though
Adding the 1st and 3rd, we get 3+9 = 12 and that is greater than the 2nd side 6.
Adding the 2nd and 3rd, we get 6+9 = 15 and that is greater than the 1st side 3.

However it does not matter that those two sums are greater, all three sums must
be greater than the remaining side.  So (3,6,9) CANNOT be the lengths of the
sides of a triangle.

Answer: d.

Edwin