To determine the color of solutions for compounds like Co(NO3)2, KMnO4, Na2Cr2O7, and ZnCl2, it is essential to memorize the basic colors associated with these compounds. ZnCl2 is noted for forming a colorless solution when dissolved in water, while other compounds exhibit distinct colors. The discussion highlights the importance of oxidation states in influencing the color of compounds, particularly with copper. Additionally, participants suggest utilizing resources like Wikipedia for reference and emphasize the relevance of crystal field theory and ligand arrangements in understanding these colors. Overall, understanding these principles is crucial for accurately identifying solution colors in chemistry.