Lot of ambiguity in the question.

For example:

Did the child live for half as long as he had at that point, or half as long as he did in total, including 4 years?

If the child lived half as long as he did, at that point, then

x = X/6 + x/7 + x/12 + 5 until he got married

x = x * 33/84 + 5.

For the child to be half his age would require the child to be x * 33/84 + 5 old when he dies.

So at the time the child dies, the man is twice that.

x = x * 66/84 + 10

And he lives 4 more years.

x = x * 66/84 + 14

18/84 * x = 14

x = 65 & 1/3, quite a bit different from the 84 years you get from the contrary bumumption!

In fact, there are 32 different possible interpretations of the question. Very badly worded.