I don't get what this means at all. Can you try to Eli5

To figure out how far a distance you traveled to get to my house, I need to know which path you took.

To figure out how long a time you traveled to get to my house, I need to know which path you took.

Our ordinary intuition is instead,

"To figure out how long a time you traveled to get to my house, I need to know the time on my clock when you left and the time on my clock when you arrived."

But that turns out to be wrong if you care about a high degree of precision or if you were traveling very fast.

Also because there is no meaning for the first value (there is no “synchronicity” between separate clocks).

Might be reasonable, but it means that comparing timestamps between two observers requires knowing the observers' entire history back to some reference timestamp no? Still a headache.

Also, if we added the speed of light to an object's speed you'd get really weird results like you'd see a car coming towards you before the car actually arrived.

Trying to stay alive in such a world would be quite a challenge.

All the cars I see coming, I see them before they arrive

I meant like this: https://youtu.be/_pEiA0-r5A8

You would see the image of a car before the actual car arrived

Cars are not superluminal.