I have an LG flat screen TV for 8 months
Lately, I have noticed that a thick black line to the right and it's far about 5 cm from the extreme right
And this line goes and come back the whole time
What to do ?

If its under warranty take it back, if its not call a repair shop and find out if it will cost less to repair than to replace.

Ask some maintainer to help you solve this problem or call the customer service

I give the poster a near zero possibility they will be able to fix it themselves. If they are asking on a forum, they likely have no electronics training, not electronics test equipment, and no experience working on electronic components and sub-assemblies. And you can't teach this in a thread..it takes years of specialized education and even more years of practical experience to learn.

Also given the nature of consumer electronics these days... its likely to cost more to repair than replace. No repair shop is going to even look at it without an up front fee... (which is usually applied towards the repair bill if you get it fixed) because time is money, and they would quickly be out of business if they did it free given the numbers of people that would decide to buy a new one.

Speeking as someone who does have such equipment, does have an Electronuic Engineering degree, and has worked on my own TV's over the last 30 years. And I don't even bother to fix my own any longer when they break, because by the time I buy the schematics, spend a lot of my time to find the problem, I usually find the parts needed will cost a significant percentage of what a NEW TV will cost just to repair a TV that is several years old or more and have worse or fewer features than the new one. And that's not even covering what my time is worth, even to myself.

Depending on where they live....it might still be under warranty ( some countries I have seen have far less generous warranty periods than others for even the same Manufacturer, which I hope it is for them.

A TV hasn't been a user servicible item by untrained people since they all had tubes, that you could simply plug into a tube tester at a store and replace them if they failed....and they haven't had tubes since the 1970's. The EARLY 1970's.

And I am old enough to have owned and worked on Tube type TV's in my youth even if they stopped making them long before I went to college. My first few tv's were used tv's. As well as what my parents had that I worked on before them.