Interfacing BT Module HC-06 and GSM Module SIM 808 EVB-V3.2.2 at the same time

For starters, you are using two serial devices, both on software serial. Your Mega has four hardware serial ports, yes, four, and you are using only one of them - and that is just for the monitor. That cannot possibly be a good idea.

Your output does indeed look like mis-match in baud rate but everything seems to be at default 9600, and you only have to ensure the serial monitor or terminal is set at 9600 too.

So I know that the baud rate of the SoftwareSerial should be like 10 times higher then the one from the altSoftSerial port.

This sounds like complete nonsense, and is irrelevant anyway.