Let's analyze the given information step-by-step to determine the possible age of L:

• Only two people are older than M: This means M is the third oldest.
• Only two people are younger than K: This means K is the third youngest.
• The age of K is a multiple of 10: Considering the other ages, K's age can be 20 or 30. But later we find that K is the third youngest, so K must be 20 years old.
• The youngest is 12 years old: Let's denote the youngest person as Y. So Y = 12 years old.
• F is the eldest: This gives us an upper limit for the ages.
• N is older than L, but younger than H: This places N and H between other people in the age ranking.
• L is not the youngest: This eliminates the possibility of L being 12.
• The sum of the ages of the youngest and second oldest person is 42 years: Y + second oldest = 42. Since Y = 12, the second oldest person is 30 years old.

Now let's arrange the ages in ascending order: Youngest (12), Second Youngest (?), K (20), M, N, H, Eldest (F).

Since K is the third youngest and is 20, and the youngest is 12, the possible ages must be 12, 13, 14, 15, 16, 17... We know the second oldest is 30. We can logically deduce the ages of the remaining people to satisfy all given conditions. Considering the sum of the youngest (12) and second oldest (30) is 42, this places K as third youngest (20) and M as third oldest.

Considering all conditions, the only possible age for L that fits this arrangement is 15 years. This would make the age order: 12, 15, 20, M, N, H, F (The order of M, N, H, and F can be further narrowed down but is not required to find L's age).