"To like for somebody/something to be something" vs. "to like somebody/something to be something"

Solution 1:

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.

Solution 2:

There is no effective difference in terms of meaning. Both can be used interchangeably, though the first sounds more formal ( this isn't to say it is formal )