Working $12\text{hours}$ per day, Yashu can copy a book in $20\text{days}$. How many hours per day should he work to finish the work in $16\text{days}$?

We can use the work formula:
$$M_1\times D_1\times H_1=M_2\times D_2\times H_2$$

Since the person doing the work is the same ($M_1=M_2=1$), the formula simplifies to:

$$D_1\times H_1=D_2\times H_2$$

Given:
$D_1=20\text{days}$
$H_1=12\text{hours/day}$
$D_2=16\text{days}$
Let $H_2$ be the required hours per day.

Substitute the values:

$$20\times 12=16\times H_2$$

$$240=16\times H_2$$

$$H_2=\frac{240}{16}=15\text{hours/day}$$

Therefore, he should work $15\text{hours}$ per day.