I got 2008 LX 570 last week, but shocks probably broken, ride is so bouncy.

Rear and Front in total is $3200, is that a good price or too much?

 

They are definitely overcharging you for parts.
Retail on the fronts is $270 ea (Can be had for $200 online)
Retail on the rears is $75 ea (Can be had for $53 online)

They are are a pain to change because of the hydraulic system. You would need to depressurize the system before disconnecting.
You would also need to change the fluid which is fairly expensive.

You would have to decide of the labor is acceptable but that is way to high for parts.

Are the shocks leaking? That is pretty much the only reason you would need to replace them.
Have you tried changing the comfort level using the switch on the right. There are 3 levels and the firmest one is fairly firm.

 

I have tried the comfort level, but nothing felt any different.

After they changed the front, shop decided not to finish the rear said too much work for them... seems like I have to bring my vehicle to Lexus dealer.

 

Can it be those (I don't know what they are called) circular drums (I think u have 2 or 4 of them?) underneath the vehicle where the center pillars are.

 

The accumulator globes is what z32 is referring to.
I don't understand why the shop gave up. Once the system is depressurized and disconnected, changing the shocks is like on most any other vehicle. Unless yours are pretty rusted.
I would look for an indy shop that knows Toyotas. They may be familiar with the AHC system.

 

...and if they're not familiar with the AHC, find another indy shop or take it to a dealer.

 

When I usually hear people having a real bouncy suspension it usually is the accumulator globes they end up replacing. I don't know if that is better or worse, but just make sure you are paying to fix the right parts. Also, I hear the rear shocks are a nightmare to remove.

 

Just wondering 'how bouncy' it should feel (assuming due to failed accumulators)?

 

I can't say. My AHC system is ok so far. But on the threads I read on IH8MUD people who complain about being bouncy (I assume they mean multiple bounces after a bump) usually are told they need new accumulator globes, not shocks. I don't know if the OP assumed the shocks were the problem or if the repair shop diagnosed them. I don't know if this shop knows what it is doing, especially since they abandoned the rear shock replacement. If I were OP I would get the AHC looked at by someone who knows them and determine what the real problem is. No sense replacing $3500 of shocks and then still have to spend thousands more to replace the globes because they were the actual problem.