breed, care for, shepherd, feed, pasture
牧 centers on tending and raising animals: breeding, feeding, shepherding, and caring for livestock on pasture.
牧 combines 牜 (cow) and 攵 (a hand holding a stick), suggesting a hand herding cattle. This is a standard phono-semantic compound where 攵 may also hint at the sound.
A cow (牜) on the left and a hand with a stick (攵) on the right: picture a shepherd using a staff to guide cattle across a pasture.
For ボク, imagine a shepherd herding cattle while wearing a pair of boxy boots: box -> ボク, and the boots help him walk the pasture.
farm (livestock); stock farm; ranch; station
pastor; minister; clergyman; reverend
pasture; grazing land
regional governor in ancient China
pasture land; ranch
pasturage; grazing
pasture; grass
shepherd's song
nomad
sheep farming
stock-farming; livestock farming; cattle breeding
nomadism
herder; herdsman; shepherd
OK; sure; certainly; no problem
Old MacDonald Had a Farm (children's song)
bear farm; bear ranch
vicar
associate pastor; curate
governor (of an ancient Chinese province)
military chaplain