Let there be $24$(LCM(6,4)) pages in the book.
Ananth takes $6$ hours to read $24$ pages $\Rightarrow$ Ananth takes $1$ hour to read $4$ pages.i.e. $20$ pages still left to read
Bharath takes $4$ hours to read $24$ pages $\Rightarrow$ Bharath takes $1$ hour to read $6$ pages i.e.$18$ pages still left to read
After how many hours number of pages to be read by Ananth, twice that to be read by Bharath.
Option $A.$ $1$ hour
It is not the answer since $20 \neq 2*18$
Option $B.$ $2$ hour
In $2$ hour Ananth will read $8$ page so $16$ pages will be left
In $2$ hours Bharath will read $12$ pages and $12$ pages will be left.
$\because$ $16 \neq 2*12$
$\therefore$ Option $B$ is not the answer
Option $C.$ $3$ hour
In $3$ hours Ananth will read $12$ page so $12$ pages will be left
In $3$ hours Bharath will read $18$ pages and $6$ pages will be left.
$\because$ $12 =2*6$
$\therefore$ Option $C$ is the correct answer
$\therefore$ Option $C.$ $3$ is the correct answer