I wrote :
Hezbollah might carry out some terrorist attacks 40 years ago against a known enemy to them. But what about now.
I meant that is possible (however not surely). Which tense of verb should I use.
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As is, your sentence talks about a possible action in present which is inconsistent with 40 years ago.
Since the action occurred in the past (40 years ago) you need may + perfect infinitive:
may have carried out...
This construction talks about the possibility that something happened in the past. It could also be used to say that something was true in the past.
If you were to use might +perfect infinitive, that is:
might have carried out...
then this construction would talk about past events or situations that were possible but did not happen.