It may be possible to get a glimpse of what 2D or 4D would look like, although it would probably be very difficult.
However, we can to some degree "feel" 2D and 4D.
For example, if you have ever played a 2-dimensional platformer video game then you have probably found yourself thinking of the 2-dimensional environment as very natural - if you see an obstacle, you just intuitively know that you must walk under it or above it in order to continue, and you don't even consider the possibility "maybe there is a 3:rd dimension that would allow me to pass through this object?", you just accept that there are only 2 dimensions.
Also, when I try to understand 4D I will usually try to think of it as a bunch of parallel universes, stacked together in a hyperspace, and that all life in this universe are in a certain location in that hyperspace.
For example, if you have access to the 4:th dimension in everyday life then you could use it to walk some distance in that direction, then walk "normally" in that space until you wanted to return to this space again.
That's how the 4:th dimension would allow you to walk through solid objects - just leave this plane of existence an walk some distance in a parallel universe, and then come back here again.
The computer game "Miegakure" has made a great demonstration of this phenomenon.
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