We will first start by knowing the concepts of squaring a number before we begin to solve the problem. Basically, squaring a number means multiplying a number with itself to get a perfect square (a number which can be expressed as a square of any other number). For example, we have the following numbers (1, 2, 3 and 4). Now squaring them means multiplying these numbers by themselves, doing so, we get $1\times 1=1$, $2\times 2=4$, $3\times 3=9$ and $4\times 4=16$. Now, coming back to the problem in hand, we need to find the numbers that lie between squares of 12 and 13. Thus, we first find the squares of 12 and 13. We have, $12\times 12=144$ and $13\times 13=169$. Now, we need to find the numbers between 144 and 169. The numbers between 144 and 169 are 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167 and 168. We can clearly see that there are 24 numbers (by counting the enlisted numbers).