The sentence is:
I’d encourage everyone to read as far into these sections as interest and patience allow.
Why it's "read ... into" and not simply "read", like this sentence:
I’d encourage everyone to read these sections as far as interest and patience allow.
I found it confusing mostly because my dictionary says the phrasal verb "read into" implies a negative meaning:
read into [read sth into sth]: think that a situation, action etc has a meaning or importance that it does not really have
The first example is not the phrasal verb read into; it's the verb read, followed by the preposition into.
Where are the students supposed to read? Far into the sections.
Not all word combinations that make up phrasal verbs are phrasal verbs. Correct parsing is essential. For example, the phrase go far has its own entry in the dictionary. However, in the sentence:
We had to go far down the road before we finally found a gas station.
the words go and far are not linked together. We might have just as well said:
We had to walk far down the road before we finally found a gas station.
or:
We had to go a long way down the road before we finally found a gas station.
If one of the words in a possible phrasal verb can be substututed with a synonym, then it's probably not a phrasal verb. In your sentence, we could reprhase it as:
I’d encourage everyone to study as far into these sections as interest and patience allow.
I think the intended meaning becomes clearer if you associate "into" with "as far" instead of associating it with "read"
I’d encourage everyone to read as far into these sections as interest and patience allow.
This would remove the ambiguity:
I’d encourage everyone to read as much of these sections as interest and patience allow.
