How to say "Let me help you"?

[cebrax]

So, yesterday, I met a guy, a Syrian. He knew English very well, however I tried to speak with him in Arabic as far as you guys thought me until the lesson "#116 - Beginner - Wrong Bus". And I should say I could say a lot of things that are very practical and useful, thank you for that. Also, he understood that I am learning Arabic and helped me by trying to talk in Arabic, as much as he can.

He was going to the airport and was carrying a small baggage. I tried to offer him to carry his baggage after we greeted each other and introduced ourselves. I wanted to say "let me help you". However, I couldn't.
I tried with اسمحي ان اساعدك and asked him if I used that correct, he told me "no", and told me how to say it in proper way and I forgot what he said.
I looked up Google Translate and it came up with this answer: اسمحوا لي أن تساعدك.

Now, could you break things down for me? Also, I am curious why تساعدك is used. Doesn't it mean "you help you"?

[Ehab]

Well, first thing Google is wrong!! Yes, although it is google, but it is still a computer that can't translate things as good as human.

In your first sentence you just missed one letter.. You know that (isma7 إسمح) means (allow-permit), now you need to say (allow me - permit me), so you just add (lee لي) so the correct way of saying that is simply:
إسمح لي أن أساعدك

Notice that people sometimes join (إسمح) with (لي) so it becomes (إسمحلي) but the proper way is to separate them.

Hope that helps.

[cebrax]

Oh, thank you for your answer. It is very relieving and helpful for me.

However, one of my cousins studied Arabic language and literature in the college. She told me that correct form should be:

اسمحوا لي أن تساعدك

It is really bugging me now. Is this form also correct?

Again, thank you a lot.

[Moshaya]

The literal translation for

اسمحوا لي أن تساعدك
You all permit me to you/she help you

تساعدك here doesn't make sense, because the first letter ت indicates you or she, and the letter ك at the end indicates that you are talking to one person, so اسمحوا wouldn't fit here as it's talking to a group of people

The correct form is

اسمح لي أن أساعدك
Allow me to help you (talking to one person)

or

اسمحوا لي أن أساعدكم
Allow me to help you all (Talking to more that two persons)

[cebrax]

Oh, I get it, this is the explanation I was guessing but was not sure of. Both of the masters said it was wrong, so I guess I should tell my cousin the correct form.

Thank you Ehab and Mohammad for your very helpful and detailed answers.

With help of you guys, I can now understand Arabic in beginner level, and I've started from scratch! I cannot thank you guys enough.