Connecting multiple thermocouples to a single interface (e.g. MAX31855) would require a multiplexer chip with specs that are good enough that you don't lose too much precision. It's possible but not really practical.
If you're really strained for money you could use HX711 modules (~$1) as amplifiers and program the Arduino to calculate the temperature from the readings provided by the HX711. But again it would require more programming effort on your part and a bit of calibrating to get right.
I was misunderstood, I meant connect 1:1 thermocouple and MAX31855 (6 thermocouples to 6 different MAX31855) and then connect my 6 MAX31855 to Arduino.
These are SPI devices (you will want to spend a few moments learning how SPI works). Each chip will require a separate pin (any pin) on the Arduino for the "CS" pin (AKA "Chip Select" or SS for "Slave Select").
cellax:
I think I miss the power supply and logic level specs.
It seems that I cannot use connecting it directly to Mega2560 because it works at 3.3 Volt.
You're correct.
You can either buy level converters, as the tutorial shows, or you can buy an Arduino variant that operates at 3.3V. If you go the level converter route you will need 2 channels (SCK and SO/MISO) which will connect to all the amplifiers then 8 channels for the CS on each amplifier; 10 total.
Some level converters do not have a 3.3V regulator on them. The one in the tutorial does, but the less expensive (and just as good) mosfet-based converters will need a 3.3V connection between the Arduino 3.3V and the converter 3.3V.