One of the most annoying defensive/offensive structure is the Aramonian Trebuchet and, fortunately, Zhon seems to have a greater advantage against this structure than the other three kingdoms (Taros, Veruna, Creon). Zhon hasn't as much buildings as the other kingdoms, so the Trebuchet is not as deadly as it is against the Taros, Veruna and Creon. However, Trebs can always become a thorn in your back, so here are some tips which I hope will help to deal with them.
1] When you see your ground units or structures to be hitted by something that looks like an extremely-fast moving cannonbal it is by 95% a Trebuchet. The first thing you should do is to detect the way from where that "cannonball" came. It is not an easy thing to detect its coming direction, you actually can only notice the moving Trebuchet's projective just before it hits you, but you must!
2] After detecting its direction, quickly create an aerial scout (Bat in Zhon) and send it flying towards the Trebuchet's direction. Sooner or later, you will notice a big wooden structure with a round stone base. This is the Trebuchet. If your Bat is killed by Archers or something else before you locate the structure, make a few more Bats and send them all together. Luckily, someone will survive to see the Treb's location.
3] Deal with the problem! Destroy the Trebuchet!! This may be an easy or an extremely difficult task, depends on how well the Aramon player guards this engine of destruction. The most common way is to create a dozen of your fastest ground unit (Spirit Wolf) and send them alltogether against the Treb.
4] In case the upper strategy doesn't work because the Aramonian defenses are too strong (many Strongholds or a lot of infantry for example) or because the terrain makes it impossible (aquatic maps for example) you should make an aerial assault using along the variety of Zhonian air combat units (Gryphons are mostly recommended, although Wisps and Drakes will also do the work). Create a dozen of them. Since the Aramon has no offensive air units at all, you will probably encounter minimum resistance while your air fleet flies towards the Trebuchet and ruin it apart. However, a group of Guard Towers and Mage Archers can wipe out your Zhonian air force fairly easy, so be careful!
5] In some cases the best way to destroy an Aramonian Trebuchet is the Zhonian moving siege tower, known as Stone Giant. Just create a pair or more Stone giants and throw rocks against the Treb without mercy. Just built them as fast as possible (the use of multiple Beast Lords is highly effective, if you have the mana of course) and don't build them too far away from your target, since Stone Giants are slow. Don't forget to have a small guard force around your Beast Lords (Trolls may be the best choice here). Despite the fact that Beast Lords are not weak, they will not stand against an unpredicted enemy assault without any help (let alone the fact they cannot attack and build at the same time). I suggest to use this strategy only if the above ones have a very low chance of success.
6] If you play on an aquatic map and the Trebuchet is near the coast, a group of Krakens or a force of Swamp Beasts coming out of the water is a good strategy to get rid of your nemesis.
7] Another way to destroy a Trebuchet is with your Roc. Just create a few Rocs, load them with troops (Goblins and Giant Orms are mostly recommended) fly above the map and upload them right next to the Treb. Goblins and, especially, Giant Orms have bonus against buildings, so they will destroy it in no time.
8] A non-reccomended tactic that should be used wisely is to destroy the Aramonian Trebuchet with your Thirsa. With a combination of her 1st and 2nd attack, she can take the structure down fairly quickly. However, don't forget that Thirsa is fast and can fly, but she is also unique and weak, so it would be a shame to lose her by the Aramonian defences just for a silly Treb.
9] Here is some extra info about the trebuchet:
* Trebuchets cost more than 10000 mana and are slow in production, so if you destroy it before it act your opponent will lose a lot of time and a lot of mana for nothing!
* Trebuchets have tremendous range! In small maps, they can easily hit any ground/naval unit or building. However, they cannot hit aerial units and in big maps you can keep your ground/naval units safe by leading them out of the Treb's range.
* Trebs are rediculously fragile. It is by far the Aramonian building with the less hit points (if you exclude Lodestones), so they can be destroyed really fast.
* Aramon players usually use Flying Builders to construct Trebs to the most unpredictable places. Always search every single inch of the map for Trebuchets, you never know where they may be...