How does the processes of photosynthesis and cellular respiration allow for the flow of energy in organisms

Photosynthesis and cellular respiration go hand and hand. Remember the two equations are just a reverse of the opposite equation.

Cellular Respiration-

C₆H₁₂O₆ + 6O₂ (Yeilds or Makes) 6CO₂ + 6H₂O + ATP (Or Energy)

Photosynthesis-

6CO₂ + 6H₂O + ATP (Or Sunlight) (Yeilds or Makes) C₆H₁₂O₆ + 6O ₂

When a plant goes through photosynthesis it produces oxygen as a waste product, which you should know is what animals use to breathe, well when animals use oxygen in the process, they also make a waste product which happens to be Carbon Dioxide, which a plant uses to make glucose during photosynthesis, so if we didin't have one we wouldn't have the other.