Three sets of books on Maths, Science and Social Studies have $240$, $336$ and $96$ books in each set respectively. The books need to be stacked in such a way that all the books are stacked subject-wise and number of books in each stack is same. The total minimum number of stacks will then be,

To find the minimum number of stacks, we must maximize the number of books in each stack. The maximum number of books per stack must be the Highest Common Factor ($\text{HCF}$) of the quantities of the books: $240$, $336$, and $96$.
Let's compute $\text{HCF}(240,336,96)$:

$$240=48\times 5$$

$$336=48\times 7$$

$$96=48\times 2$$

Thus, $\text{HCF}=48$. This means each stack will contain $48$ books.

Now, we calculate the number of stacks required for each subject:

* $\text{Maths Stacks}=\frac{240}{48}=5$
* $\text{Science Stacks}=\frac{336}{48}=7$
* $\text{Social Studies Stacks}=\frac{96}{48}=2$

$$\text{Total minimum number of stacks}=5+7+2=14$$