The area of a square field is 8 hectares.

We know that 1 hectare = 10000 m2.
So, Area of square field = 8 hectares = 80000 m2.

$\Rightarrow \frac{1}{2}(\text { diagonal })^{2}=80000$

$\Rightarrow(\text { diagonal })^{2}=160000$

$\Rightarrow$ diagonal $=\sqrt{160000}=400 \mathrm{~m} .$

Now, distance to be travelled = 400 m

speed is given to be $4 \mathrm{~km} / \mathrm{h}=4 \times \frac{1000 \mathrm{~m}}{60 \mathrm{~min}}=\frac{4000}{60} \mathrm{~m} / \mathrm{min}=\frac{200}{3} \mathrm{~m} / \mathrm{min}$

Therefore, time taken $=\frac{\text { distance }}{\text { speed }}=\frac{400}{\frac{200}{3}}=\frac{400 \times 3}{200}=6$ minutes.