I am trying to understand syncopation and in this case the forth beat is a a weak beat. There's no rest before it but a half note (minim). Is this a case of syncopation? I was trying to train myself on understanding beats and tried a quiz here and bump
Possibly going to be a little subjective. But basically, syncopation means shifting the emphasis from the expected beats 1 and 3 (in 4/4) to other parts of the bar, including a simple example such as you quote. Often syncopation is a little more complex than that, with a good chance that some would lose their way, and end up at the wrong place in a 'standard' bar later - I know - I've been there!
The way I learned it, a syncopated note is one that occurs on a weak division and there's no note on the strong division immediately following it.
So in your example, the half note is an example of syncopation (it anticipates the strong third beat), but we can't know if the final quarter note is without knowing if there's an attack on beat 1 of the following measure.
I've found this definition consistent with what "feels" like syncopation, so I feel comfortable passing it on, but I'll gladly update with a source if anyone can find one (including the Adam Neely video I probably got it from).