Build

Bobby can build a house in $24$ days, this means that he can build $\dfrac{1}{24}$ of a house in $1$ day.

Similarly, Danny can build $\dfrac{1}{36}$ of a house in a day, and Andy can build $\dfrac{1}{27}$ of a house in a day.

Now, Bobby and Danny worked together for $8$ days. Each day, they can build $\dfrac{1}{24} + \dfrac{1}{36} = \dfrac{5}{72}$ of a house. In the $8$ days they worked together, they built $8 \times \dfrac{5}{72} = \dfrac{5}{9}$ of a house.

The rest of the work will be continued and finished by Andy. This means that Andy has $1 - \dfrac{5}{9} = \dfrac{4}{9}$ of the house remaining to build. Now, let the time taken by Andy be $x$ days. We know that:

$\dfrac{1}{27} \times x = \dfrac{4}{9}$

Therefore,

$x = \dfrac{4}{9} \times 27 = \boxed{12}$

Note: The wording of the question seems a bit off to me. When the question says "how long does it take to finish their job", I would assume that the question is asking the total time taken by the 3 of them to finish it in that manner. A better way to phrase it would be: "how long does Andy take to complete the remaining work"

Good question, tons of people in my class get that one wrong!!! (sometimes including me)