$A$ takes $6$ hours more than $B$ to cover a distance of $60\text{ km}$. But if $A$ doubles his speed, he takes $3$ hours less than $B$ to cover the same distance. The speed (in $\text{km/hr}$) of $A$ is:

Let the speed of $A$ be $v\text{ km/hr}$.Initially, time taken by $A$ to cover $60\text{ km}$ is $\frac{60}{v}$.When $A$ doubles his speed, the new speed is $2v$, and time taken is $\frac{60}{2v}=\frac{30}{v}$.The difference in time taken by $A$ between the two scenarios is:
$$6\text{ hours (more than B)}+3\text{ hours (less than B)}=9\text{ hours}$$
Thus,
$$\frac{60}{v}-\frac{30}{v}=9$$
$$\frac{30}{v}=9⟹v=\frac{30}{9}=\frac{10}{3}=3\frac{1}{3}\text{ km/hr}$$