6 years ago, I was in Bangladesh for 2 years / I spent 2 years in Bangladesh.
Use the past simple tense because this is finished.

I was able to go there through KOICA (Korea International Cooperation Agency).
From "to be able to".

I built my classroom, and taught Korean to Bangali students.

Whenever I had time, I went around the small town, talked with people over a cup of milk tea (they call it "Chai"), and I gave them soap out.
'their' is incorrect. You can't really say 'them' yet because this is the first time you mention people. If you mean that you visited your students, you should say that: "talked to my students". If you mean people from the town, say "people".
In "to give out", 'give' and 'out' must be together. You can say "I gave out soap" or "I gave them soap", although these have slightly different meanings.

In Bangladesh the weather is very hot, and the humidity is also high.

My first day in Bangladesh, I was so tired even sitting in a chair, but I quickly got accustomed to life there.
This sounds more natural.

Of course there were some small incidents such as muggings / theft.
"to meet robbers" doesn't sound right. I think it's better to talk about the crime: theft or mugging (where something is stolen from you in the street).

But almost people there are very kind and attentive.

I often remember them, and missing them.

An invaluable experience of my life (don't need) 

6 years ago, I went have been in to Bangladesh.  I was there for 2 years.
I could was able to go there through KOICA(Korea International Cooperation Agency).
I built my classroom, and taught Korean to Bangali students.
Whenever I have had time, I went around the small town and talked with people thier over a cup of milk tea(they call called "Chai").  In exchange, I gave them soap.

Bangladesh wheather is very hot, and the humidity is also high.
The first day of arriving I arrived in Bangladesh, I was very tired (even sit chair ?), but I quickly accustomed there to life there.

Of course there was were some small accidents unfortunate incidents, for example being robbed. as to met robber.  
But almost everyone of them are was very kind and attentive.

I often remember them, and missing them.

AN INVALUABLE EXPERIENCE

Six years ago, I spent two years in Bangladesh. I was able to go there through KOICA (Korea International Cooperation Agency). While I was there, I established a classroom and taught Korean to Bangladeshi students. Whenever I had time, I would travel around the small town, talk with the locals over a cup of milk tea (they call it "Chai"), and I sometimes gave out soap. The weather in Bangladesh is very hot, and the humidity level is high. During my first day in Bangladesh, I was so tired even when sitting in a chair, but I quickly became accustomed to life there. Of course there were some unfortunate incidents with thief and muggers. But most of the people there were very kind and attentive. I often remember them, and miss them.