Student or Learner
In the above link, there is a video, whose beginning is quite confusing to me.
As I heard, "It was one of those moments which mattered much more to picture desks and photographers than it did to the principals. William was only nine when his mother visited the Taj Mahal."
I am not sure the underlined part. Can any native teacher help me to hear it out correctly?
You heard it correctly. It means that the moment in question (the couple visiting the Taj Mahal) was less important to the couple than it was to the photographers who were present and to the departments of national and international newspapers which deal with photographs. Those are "picture desks" - the desks at which newspaper employees sit and sort through/edit/choose which photos will go in the newspaper.
Every news station in the UK made a really big deal out of the fact that Princess Diana visited the Taj Mahal alone in the 1980s, and was photographed there looking very sad and lonely (it wasn't really a well known fact at that time that her marriage to Prince Charles was on the rocks but it was a very big clue!). The reporter is trying to say that although the media were very interested in making the connection between the previous visit of Princess Diana and the current visit of her son and his wife, it's likely that William and Kate really weren't that bothered about the connection, but were simply enjoying their trip around India.
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.