Serial Communication over Desktop to Arduino
I have a USB 2 Serial adapter...I have connected the TX0 pin of Arduino to DB 2 pin (read pin) of the adapter.


You must not connect Arduino pins directly to a D-SUB connector of a USB-Serial adapter, as those connectors traditionally carry higher voltage, opposite sense RS232 signals.


The voltage is too high, and likely to cause damage to your Arduino's processor
The signal is inverted in sense from the logic-level signaling used by your Arduino's processor.


If you actually needed to make this connection, you would need to either use a "logic level" USB serial adapter (sometimes informally called a USB-TTL adapter).  These terminate in various types of connections such as bare wires or header pins/sockets - but basically never in an D-SUB connector.  Or you can use an inverting line driver and receiver such as the MAX2232 type devices, or even an old 1488/1489 pair.

But it's not clear that you should be doing this at all - an Arduino Mega already has a USB-serial converter onboard - that is the interface you use to program it, and it would ordinarily be simplest to use that for runtime communication as well.