After the verb like, and other verbs of preference or intention, an infinitive object complement clause requires a For..To-complementizer on its verb

• I would like to go., but not
• *I would like go.

and like optionally allows a For-complementizer to mark the subject of an infinitive complement, if it's different from the subject of like

• I would like for him to go ~ I would like him to go.

This is all summed up in the formula below, with optional for in parentheses:

• I would like (for) him to go

Similarly,

• I intend (for) him to become an engineer.
• I prefer (for) you not to leave.
• I want (for) you to go tomorrow.enter link description here

Normally, though, the for of the For...To infinitive complementizer gets deleted.

After the verb like, and other verbs of preference or intention, an infinitive object complement clause requires a For..To-complementizer on its verb

• I would like to go, but not
• *I would like go.

and like optionally allows a For-complementizer to mark the subject of an infinitive complement, if it's different from the subject of like

• I would like for him to go ~ I would like him to go.

This is all summed up in the formula below, with optional for in parentheses:

• I would like (for) him to go

Similarly,

• I intend (for) him to become an engineer.
• I prefer (for) you not to leave.
• I want (for) you to go tomorrow.enter link description here

Normally, though, the for part of the For...To infinitive complementizer gets deleted. This is not surprising, because the subject noun phrases of infinitives are often deleted, with their complementizer, of course.

After the verb like, an infinitive object complement clause requires a To-complementizer on its verb

• I would like to go. ~ *I would like go.

and allows a For-complementizer on its subject, if it's different from the subject of like

• I would like for him to go ~ I would like him to go.

This is also true of some other verbs of preference or intention

• I intend (for) him to become an engineer.
• I prefer (for) you not to leave.
• I want (for) you to go tomorrow.

Normally, though, the for of the For...To infinitive complementizer gets deleted.

After the verb like, and other verbs of preference or intention, an infinitive object complement clause requires a For..To-complementizer on its verb

• I would like to go., but not
• *I would like go.

and like optionally allows a For-complementizer to mark the subject of an infinitive complement, if it's different from the subject of like

• I would like for him to go ~ I would like him to go.

This is all summed up in the formula below, with optional for in parentheses:

• I would like (for) him to go

Similarly,

• I intend (for) him to become an engineer.
• I prefer (for) you not to leave.
• I want (for) you to go tomorrow.enter link description here

Normally, though, the for of the For...To infinitive complementizer gets deleted.