受…影响 / 受到…的影响【shòu…yǐngxiǎng / shòudào…de yǐngxiǎng】

受 means "receive" or "undergo", so 受…影响 is literally "receive X's influence". The thing affected is the subject and the cause sits in the middle. 的 between the cause and 影响 is optional, and more usual after a longer cause.

受到 is the fuller, more written form, and it usually takes 的: 受到了…的影响.

At the start of the sentence

受…影响 can open a sentence and give the cause of what follows. News reports and announcements use it constantly.

How much it was affected

The size of the effect goes after 影响 as a comment – 很大, 不大 – or in front of it as 很大的. It doesn't go between 受 and the cause.

• × 他受很大父亲的影响 → 他受父亲的影响很大

The cause goes in the middle

English "influenced by his teacher" puts the cause last. In Chinese the cause sits between 受 and 影响.

• × 他受影响他的老师 → 他受他老师的影响

To make the cause the subject instead, use 对…影响: 父亲对他的影响很大 "his father had a big influence on him".

受…欢迎 "be popular with" uses the same frame: 这本书很受年轻人欢迎.