The shepherd boy rode an ox herding in the fields.
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memory
牧 combines 牛 (cow) on the left and 攵 (hand with stick) on the right - a hand driving cattle. This image appears in many pastoral words: 牧场 (ranch), 牧师 (pastor), 牧民 (herder).
Cow on the left is the object being herded. The indexing form 牜 used in dictionary lookup is just the left-side variant of 牛; visually here 牛 stands clean and intact, depicting the head and horns of an ox.
Right side shows a hand with a stick - the action component, sometimes called 'rap'. Combined with 牛 it paints the literal scene of a herdsman tapping cattle along. The same action radical drives 教 teach, 攻 attack, 改 reform.
