hinschauen
to look
To deliberately direct your gaze at something or in a particular direction.
Schau mal da hin, ein Regenbogen!
Look over there, a rainbow!

to look / to look closely
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to look
To deliberately direct your gaze at something or in a particular direction.
Schau mal da hin, ein Regenbogen!
Look over there, a rainbow!

'Hinschauen' (to look / to look closely) is a separable verb. The prefix 'hin' comes at the end in a main clause. In a subordinate clause and in the infinitive, the verb stays together.
Er schaut genau hin, um keinen Fehler zu machen.
He looks closely so as not to make a mistake.
The verb has a literal and a figurative meaning. Literally, it means to direct your gaze at something. Figuratively, it means to engage with a difficult topic and not ignore it.
Du musst genau auf die Straße hinschauen.
You have to look carefully at the road.
In the figurative meaning, 'hinschauen' is often used with abstract nouns that describe a problem, for example 'bei Ungerechtigkeit' (in cases of injustice), 'bei Gewalt' (in cases of violence), or 'bei Problemen' (when there are problems).
Wir müssen bei der Umweltzerstörung endlich genau hinschauen.
We finally have to look closely at environmental destruction.
to look / watch
'schauen' and 'hinschauen' both have to do with looking. 'schauen' generally means that you direct your eyes at something or look at something. 'hinschauen' places more emphasis on direction and deliberate attention: you look right there and do not ignore it. That is why 'hinschauen' can also mean, figuratively, that you deal with a problem. If it is only about normal seeing or looking at something, 'schauen' is more natural. If attention is important, 'hinschauen' fits better.

Bei diesem Problem muss der Chef genauer hinschauen.
The boss needs to look more closely at this problem.
Nach dem Essen schauen wir noch einen Film.
After dinner, we’ll watch a film.