First off, since the problem is $480\times 12 \div 800 \times 25$ we could write it as the fraction $\displaystyle \frac{480\times 12\times 25}{800}$. There are many different approaches from here, but one of the main goals of the chapter this question is from is looking for 'nice' or 'convenient' ways numbers can be combined to help with calculations.

One thing to always remember is that $25\times 4 = 100$, so in this problem maybe you can start with $12\times 25 = 300 = 3\times 100$. Then, since $800=8\times 100$ we can start doing some nice canceling from here.

Hope this helps!