友達のお母さんにパスコンを＿＿＿＿。「借りる」
I came across this sentence in my reviews, with the hint ‘I humbly borrowed’.
Is there a difference between using お借りいたしました and お借りしました in this context? I tried the former and got it wrong, with no “You were close” message popping up allowing me to change my answer.
Hey and welcome on community forums 
I will follow the nomenclature used in Genki.
So basically, there are 2 kinds of humble speech.
謙譲語I (humble expressions) and 謙譲語II (extra modest expressions).
You use humble expressions when you want to exalt someone you are talking about.
The extra modest expressions are used when you want to show respect when talking to someone, but you are not necessarily doing something to/for him/her.
Let’s assume that you are a worker at the company. You are talking to your 課長 (部長 is more important than 課長) and say:
部長にご案内しました。
部長に案内いたしました。
They both mean that you showed the section manager around.
But the first has the nuance that you show respect to the person you are talking about (部長), and the second shows respect to the person you are talking with (課長).
It is more visible if we change the indirect object to let’s say まさむら、who is also an ordinary employee like you.
まさむらさんにご案内しました。
まさむらさんに案内いたしました。
In here the first one is incorrect because Masamura has a similar position to you and there is no need to exalt him.
And the second is correct because you talk about Masamura, but show respect to your interlocutor.
Also, if we change it a bit, you are speaking with 部長 now:
課長にご案内しました。
課長に案内いたしました。
In the first one, you exalt 課長, which might piss off 部長 who is more important and standing next to you. So its better to avoid it and use the second one, in which you exalt your conversation partner - 部長。
If you want to exalt both of them (which should be the case) and is the case most of the time, then you can go with:
課長にご案内いたしました。
Thanks! That makes a lot of sense.
This explanation was so easy to follow, from start to finish. Thank you!!
I felt like I almost got this, but then some reviews confused me again. 
Take these pairs of sentences. It seems that with different situations, both could be correct.
先生の分もお取りします。 <-- this is the correct answer in the review
先生の分もお取りいたします。
situation1) I’m talking to a teacher during a party, and I’m taking cake that he offered.
situation2) I’m talking to the dean during a party, and I’m taking cake belonging to the teacher that the dean offered me.
駅の前でお待ちします。
駅の前でお待ちいたします。<-- this is the correct answer in the review
Both of these (to me) say, “I’m humbly going to wait at the station for you”. There’s no third party so why am I extra humble? (except maybe to be a super brown-noser)
Am I missing something here?
(ここでご返事をお待ちいたします。
)
"Let’s assume that you are a worker at the company. You are talking to your 課長 (部長 is more important than 課長) and say:
部長にご案内しました。
部長に案内いたしました。
They both mean that you showed the section manager around.
But the first has the nuance that you show respect to the person you are talking about (部長), and the second shows respect to the person you are talking with (課長)."
I think it just works the same as the example above where you want to be respectful to the person you’re talking to. So 駅の前でお待ちいたします shows respect for the person you’re waiting for.