How do I decide whether the given shell and tube heat exchanger is a counter flow or parallel flow?

If the hot fluid is flowing in same direction as of cold fluid, then it is parallel heat exchanger.

Bur if the hot fluid is flowing in direction opposite to the cold fluid then it is counter flow heat exchanger.

2) If you have the information about the temperatures at inlet and outlet condition then you can find out the effectiveness. If the effectiveness is less than 50% it is mostly parallel flow heat exhanger. But if it has more than 50% than it is counterflow as effectiveness of parallel flow cannot be more than 50%. If both have effectiveness less than 50% then the greater one is counterflow heat exchanger.

3) If there are two heat exchangers in front of you with same parameters like inlet and outlet temperatures, mass flow rate. If you have to decide which one is parallel and counter flow,then the heat exchanger with larger area will be parallel flow while the one with less area will be counterflow heat exchanger.

4) If the outlet temperature of the hot fluid is less than outlet temperature of cold fluid it is definitely counterflow heat exchnager as it is possible only in counterflow heat exchanger

5) If you find out the LMTD of both heat exchangers for same mass flowrate, area then the one with higher LMTD will be counter flow heat exchanger.