～のもとで／～のもとに — Under the Wing Of

厳しい先生のもとで、彼は一流の職人になった。

Kibishii sensei no moto de, kare wa ichiryuu no shokunin ni natta.

Under a strict teacher, he became a first-class craftsman.

のもとで marks the guidance/supervision he worked under

両親の愛情のもとで育った。

Ryoushin no aijou no moto de sodatta.

I was raised under my parents' love.

のもとで shows the nurturing conditions of upbringing

秘密を守るという条件のもとに、彼は真実を話した。

Himitsu o mamoru to iu jouken no moto ni, kare wa shinjitsu o hanashita.

On the condition that the secret be kept, he told the truth.

のもとに introduces the premise/condition the action rests on