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Only what I read in the Western press. But given what I know about their reporting about India, it is hard to give them the benefit of the doubt when they attack right-wing governments running other countries.
As someone who actually designed a database with media affiliations in the past, I can seriously dispute this statement. AFAIK right-leaning Western media have enough influence to boost conservative agenda nearly everywhere. Remember, just recently Trump was a president of the USA, not least thanks to Fox Corp. In Germany we have Axel Springer, in UK there's Daily Mail etc.
When you make such confident claims, it makes sense to bring some data on the table.
Let me clarify.
When I speak of influence, I am not speaking about the influence tabloids have on people and their voting patterns. Instead, I am referring to "newspaper of record" type influence; news sources that will be used by academics and historians of the future to write the history of this era.
To expand on this a bit, the problem with right-wing media is that it is not taken seriously and a lot of it has to do with a lack of serious reporting. I find it very funny when right-wing media of one country refers to left-wing media of another country in their articles and programs because they are either unaware of local right-wing sources or simply do not trust them.
Definitions are contextual. Your definition of influence is local, mine is global. That does not make your definition factual and mine non-factual/"new."
All the biased reporting about India comes from outlets like the NYT/WP/FT/Economist/BBC etc which is then picked up by local media from both sides. So, when I refer to influential Western media outlets, those are the ones.
(I am surprised as to why you would expect someone from India to follow Fox or Daily Mail or whatever your local RW outlet is. Can you name a single "influential" RW media outlet from India?)