Which right?
Top right intake
bottom right outlet ?

 

your heater core is right side of your picture

 

When you are cleaning the cooling system you generally disconnect both run an adapter to connect the heater core hoses and then clean the heater core separately and gently regarding water pressure. This way 2 things done happen, you dont get contaminates from a dirty heater core dislodging and going through your cooling system and the opposite you don't plus not damaging the heater core using higher water pressure.

Shops that don't do this extra work generally don't know the damage caused until they finish and refill cooling system only to find the hater core of other cooling system valve and parts are not working correctly or there is temperature problem that was not necessarily there before the service.

 

ok.
I need to figure out what hoses to disconnect first.
Is it the two on the right side?
Top right = intake
Bottom right = outlet ?

 

A recommendation when removing the factory hose clamps. the temptation for ease of service it to use conventional aftermarket hose clamps. These often damage the hose from over tightening. The better replacement even over OEM is fuel injection or high pressure clamps the apply the force 360 degrees around the hose.

 

you disconnect both. I don't have the actual cooling system exactly for your MAZDA and information (I never assume absolution when service is being asked on a forum without looking at exact vehicle related service ) ALLData is currently in update mod so I can confirm exactly. But the general rule this configuration is lower outlet.