We know that 1 mile equals 1.61 kilometers.
So, we just have to use the following proportion to find the answer
[tex]\begin{gathered} \frac{10\operatorname{km}}{x}=\frac{1.61\operatorname{km}}{1mi} \\ x=\frac{10}{1.61}mi \\ x\approx6.2mi \end{gathered}[/tex]