Feel like at home.
Is it correct or must it be "feel at home"?
It is in a Euro 2012 commercial, however some experts say it's not correct.
I suspect feel like at home is a bad translation from some Polish phrase (this looks to be OP's "euro 2012 commercial", and it contains no English apart from having that title for the Youtube video).
I don't understand Polish anyway, but it's not obvious to me what a reference to home could mean in this context. Common idiomatic turns of phrase (definitely nothing to do with Euro 2012) are...
That second usage is normally "figurative". You can say you "feel at home with accounting software", for example, even if you only ever use it in the office. The point is you understand it, and are competent and familiar with using it.
EDIT: It seems my original link to "euro 2012 commercial" above is now dead. But here's another one which makes it clear that whatever Polish Sports Minister Joanna Mucha might say, the usage is probably best classified as a "glaring error".
What they were looking for was "Make yourself at home!", i.e. the imperative mood, as in the Polish "Poczuj się jak w domu", which is a shorter way of saying "Proszę się czuć jak u siebie w domu".
In coming up with a literal translation of "Poczuj się jak w domu" they produced pure Ponglish.
Another possibility is "Feel like you do at home" -- a sentence with a slightly different sense then "Feel at home."
"Fell at home" can sometimes simply mean "be comfortable with"; "feel like you do at home" can never mean this.
For example, "I feel at home doing calculus" is natural English for "I am comforable doing calculus"; "I feel like I do at home doing calculus" would be very wrong. However, you might say "Doing calculus here, I feel like I do at home" which would mean "It feels the same to do calculus here as at home."