Put in by or with.

The boy was hit ___ a stick.

Their children were frightened ___ thunder.

Her room is cleaned ___ a vacuum-cleaner.

The test will be done ___ the best pupil.

These rings were sold ___ a newcomer.

The boy was hit with a stick.

Their children were frightened by thunder.

Her room is cleaned with a vacuum-cleaner.

The test will be done by the best pupil.

These rings were sold by a newcomer.

___________

*Предлог with пишется, когда речь идет о том, каким инструментом/предметом кто-то другой совершил действие. А вот когда надо написать, кем совершено действие, мы используем предлог by.