Hi Jerry, and welcome!

Firstly, it's unlikely that you would have caused permanent damage to the Yamaha 600i by plugging the powered monitors into the speaker outputs. The 600i has circuitry inside that detects an abnormal load on a speaker output and shuts the output down. Normal operation is restored by switching off, waiting 10 seconds or so, then switching on again.

A couple of questions:

When you plug the ZLX 15P speakers into the monitor outputs of the 600i, is that the combination that you report that works?

Is it the 600i passive speakers you are using to plug into the speaker outputs when you say that no sound is coming out?

Yes..there is sound coming from my zlxp when I plugged them to the monitor output.

Also yes, no sound coming out from the 600i passive speakers when connected to speaker output of the 600i mixer.

Also, I heard a “pop” sound from the mixer when I turned on the zlxp when it’s hook up to the speaker output.

And the indicator light on the mixer is working (goes up and down) when the passive speakers are connected to the speaker output but no sound coming out.

This is from the Yamaha troubleshooting guide (which covers several listed models, but does apply also to the 600i):

No sound is heard:
Did you connect the mixer’s SPEAKERS jacks and the speakers’ input jacks using the proper speaker cables?
Did you firmly and securely connect the speaker cables?
Is a speaker other than the included speaker connected to the mixer’s SPEAKERS jacks? Please connect the included speaker (STAGEPAS 600BT: MODEL 600S; STAGEPAS 400BT: MODEL 400S).
Did you use the included speaker cables? If you use a commercially-available speaker cable with a metal-housing connector, the cable will be shorted when the connector touches other metal, resulting in no sound being produced.
Is the POWER LED flashing at intervals? There may be a short in the speaker cable or the connection may be faulty. Check that the speaker cable is not scratched and is connected properly to the mixer, then reapply the power.

I think we can say from this that connecting a mains-powered speaker (with grounded sleeve on the input jack) would cause the short circuit mentioned in the fourth of these points. It would be poor design on Yamaha's part if this caused permanent damage to the 600i mixer.

My guess is that the sound you heard from the mixer was an internal fuse blowing. Easily fixable by a dealer if so.

I used the same Yamaha cable when I connected it to the powered speakers. I opened the mixer and got out the fuse but can’t determine if it’s blown. I’ll try to replace it.

In this case, use of the Yamaha cable rather than any other make makes little difference. If I'm correct with my hunch, the 400i/600i series uses a bridge drive to the speakers, resulting in the signal being carried in opposite phases on both the core and sleeve of the cable (T and S on the plug). Connecting the cable to a powered speaker run from the mains would ground the sleeve, and hence short-circuit one side of the drive to the speakers.

I would urge you to find a multimeter to check the fuse that you removed from the mixer. If it is blown, it's very important to fit a new one of the exact same rating and type as the old one. If the fuse you removed is the one on the SUB61 circuit board, the service manual says it is T6.3AH 250V. However, that one is unlikely to be the problem in this case, as it is in the mains circuit, and you say there is power to the rest of the mixer, which there would not be if the mains fuse were blown.

I'm sorry to say that it's looking likely that service by a dealer will be necessary.

That’s what I’m thinking, I might send it to the service center...

Will this be an expensive repair?

Thank you very much for your help. I’ll keep you on the progress.