Select the most appropriate option to fill in the blank.
The farmers in this village _______ their fields with water from the river.

The process of supplying water to crops or land to help them grow through artificial channels or pipelines from a river is called irrigation.
Irrigate is the exact professional agricultural term.

Flush, flood, and soak describe general actions of water handling but do not carry the appropriate context of controlled, intentional watering for cultivation.

Hence, 'irrigate' is the most appropriate option.