H bridge module

Is it a problem if i connected the l 289n H bridge dual module to 12 volt and 2 ampere adapter for connecting 4 motors
2 at each output

Yes, of course. It's an L298N, that's your main problem. Excessive voltage drop & heat. Catch up with the times, get a MOSFET based motor driver. Such as the TB6612FNG or one of the DRVxxxx based boards.

For whether it supports your motors you didn't supply enough info.

https://www.google.com/url?sa=t&source=web&rct=j&url=http://www.handsontec.com/dataspecs/L298N%2520Motor%2520Driver.pdf&ved=2ahUKEwiN_p2W6OznAhWQTxUIHeSbCOAQFjAAegQIAhAB&usg=AOvVaw3RqKatlWCx_OOcg_CK8P5W

It says 12+ I'm talking about the ampere

4 motors of 12+ A each, a power supply of 2 A, and a controller that can barely manage 1A sustained without melting... what could possibly go wrong.

(maybe I misunderstand but your link is broken).

Read the specifications of each part. A power supply has a maximum amount of amperes it will supply, however it is very happy to supply less. Loads consume so much current at a given voltage, if it is less then the power supply can supply all is happy if not things fail and many time go up in smoke. The power supply tends to protect itself and the voltage will droop for a while which will mess up the loads causing them to have problems.

Shown above are darlington devices, both NPN and PNP. Each transistor will have about 0.7 Volt drop so a darlington configuration has two junctions so that becomes 1.4 volt drop. A H bridge with a darlington in each leg drops about 2.8V. Multiply that voltage times the current and you get the wattage you have to dissipate. You have over 33 watts to dissipate, that is a lot of heat. With a MOSFET H-Bridge with a RDSon 0f 0.001 ohms you will dissipate 0.288 watts. In conjunction your voltage drop goes to 0.024 volts, that is over 2.5 volts more for your load. That is about 20% more power that would have been burnt as heat. Uses a MOSFET H-Bridge your project will be much cooler.

gilshultz:
With a MOSFET H-Bridge with a RDSon 0f 0.001 ohms

Good luck finding one of those!

1 milliohm and below are available for MOSFETs, personally I've never used anything less than 2.2 milliohms ... yet ...

MarkT:
1 milliohm and below are available for MOSFETs, personally I've never used anything less than 2.2 milliohms ... yet ...

He was talking about an H-bridge. The pMOS is going to be the main challenge, as they should be <1 mΩ together... the lowest value Digikey gives for p-MOSETs is 1.6 mΩ. For nMOS it's lower of course, down to 0.4 mΩ. So (at least in theory) a 2 mΩ H-bridge is possible. Trace resistance and other parasitics may add more than that to the assembly.

Standard MOSFET H-bridges use 4 nFETs and a driver chip to bootstrap the high side switches. Checkout the datasheet for something like the HIP4081A H-bridge driver.