Can't pass the inspection, on the report , it said : two reason, 1- Monitor catalyst : not ready & monitor O2 - not ready.

Considering the codes you have an oxygen sensor fault ..That is the 02 problem..The monitor catalyst also is part of an exhaust issue...All are an emissions fault...Sometimes an oxygen sensor will also cause the catalyst code....You really need a OBD SCANNER to find which O2 sensor is at fault....They are located on the exhaust manifold and exhaust pipe....Auto zone should scan it for free just for the business...Vehicle should not need a catalytic converter but it is possible.....From my years of mechanical work I have found both of those codes to be a simple 0xygen sensor....Considering you have two codes it is probably Upstream and downstream sensors...Remember ...One is on the exhaust manifold and the other is mounted directly in the exhaust pipe ....normally in front of the converter...Each has a wiring connector attached to it...They screw into the pipe and EX.manifold...You can clear the fault codes just by disconnecting battery....Sometimes they won't notice if codes are cleared..

Your mechanics is correct.. but that's the short verion!

It's called a drive cycle, drive cycles can be difficult to follow under normal driving conditions. Begin by:
- Start the engine. Idle the engine in drive for two and a half minutes with the A/C and rear defroster on.
- Turn the A/C and rear defrost off, and accelerate to 55 mph at half throttle.. under 3,000 rpm
- Hold at a steady speed of 55-60 mph for 3 minutes.
- Decelerate (coast down) to 20 mph WITHOUT braking OR depressing the clutch.
- Accelerate back to 55 to 60 mph at ¾ throttle.. under 4,000 rpm
- Hold at a steady speed of 55 to 60 mph for 5 minutes.
- Decelerate (coast down) to a stop without braking.
If all other emissions systems are functioning properly, completing the drive cycle above will set the "readiness flags" required to pass the inspection. BTW, It will not hurt to perform the drive cycle 2 or 3 times before the inspection.