"Snälla, kan du läsa igenom mina svar?"
Translation:Please, can you read through my answers?
As a verb particle, igenom is always used. So you can’t say läsa genom mina svar, but you can say either han hoppade ut igenom/genom fönstret.
so, a verb can't be directly followed by "genom", whilst both (genom/igenom) can be used in other situations. right?
The preposition can be either a particle that goes with the verb, as om in tycker om. In that case it’s stressed and tied to the verb. The preposition can also just be the preposition used with the verb. Sometimes the meaning differ depending on whether it’s a phrasal verb or just a verb with a preposition.
Han hälsade på honom. (’He visited him’)
Han hälsade på honom. (’He greeted him’)
In the first example, på is stressed and is part of the phrasal verb hälsa på. In the second example, the verb is hälsa which is constructed with the preposition på. In this case the verb hälsa is stressed.
So, when igenom is a particle as in the 1st example, you have to use igenom, if it’s just a preposition, it can be either.
Vi gick igenom uppgiften. (’We went through the task’; gå igenom is a phrasal verb and igenom is stressed)
Han promenerade (i)genom staden. (’He went for a walk through the city’; genom here is unstressed and just the preposition to show where he went a for a walk, it’s not directly tied to the verb.)
You can read more here: https://en.wikipedia.org/wiki/Phrasal_verb