Can it be said like this or Is the second one correct only?
Look out outside the window
Look outside the window
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Both those sentences are grammatical (although the first is nonstandard and the second is slightly uncommon), but they have completely different meanings.
Look outside the window.
This means you should turn your gaze outside the window. (From inside the room you are in.)
It is also a common phrase, although not as common as just look out the window, and the meaning that would normally be thought of.
But the definitions of the noun lookout and the related verb phrase look out give different possible meanings:
1 : one engaged in keeping watch : WATCHMAN
2 : an elevated place or structure affording a wide view for observation
3 : a careful looking or watching
// on the lookout
4 : VIEW, OUTLOOK
5 : a matter of care or concern
look out verb
: to take care or concern oneself —used with for
// looking out for number one
(Lookout / look out) outside the window.
This could be an abbreviated sentence meaning several different things.
There's a guard outside the window.
There's an observation post outside the window.
You need to be paying attention to things while outside the window.
There is a view outside the window.
There is a matter of concern outside the window.
Take care of yourself when you are outside the window.
Those example sentences use a more common construction if any of those meanings are meant.
If the first sentence in the question is supposed to mean the same thing as the second, then it is an error.
You could say “Look outside” or “Look out the window.”
In the former phrase, one is more concerned with the act of looking outside. So, imagine someone who barged into a home and wanted to alert the people inside that something spectacular was happening outside. The person would scream, “Hey, everyone! Look outside!” So, however each one would be able to, they would each scramble to look outside, whether it be by running outside, standing in the open front door, or by opening the window blinds.
In the latter phrase, it is a more specific command directing the person to look outside through the window. It could be that the window is the only means by which the person can see what is occurring outside.
Neither of your two original suggestions are spoken in daily English.