The reason light from the most distant known galaxy, GN-z11, has taken around 13.4 billion years to reach us is due to the expansion of the universe. While light travels at a finite speed, the space it travels through can also be expanding. This expansion causes the distance between objects in the universe to increase over time.
GN-z11 is located at an enormous distance from us, approximately 13.4 billion light-years away. This means that the light we observe from GN-z11 today has been traveling through space for 13.4 billion years since it was emitted from the galaxy. However, during this time, the universe has been expanding, causing the space between GN-z11 and us to also expand.
As a result, the light emitted by GN-z11 has had to traverse a greater distance than the current distance between us and the galaxy due to the expansion of space. This is why light from GN-z11, even though it travels at nearly 300,000 kilometers per second, has taken around 13.4 billion years to reach us.
It is important to note that this phenomenon is one of the key pieces of evidence supporting the Big Bang theory, as it demonstrates the expansion of the universe over time.