Cobalt (ii) chloride hexahydrate dissolves readily in water to give a red solution

This problem is asking us to explain the chemistry of the observation that was made. The observation made was that when used in writing in paper, it would not be visible if the paper would dry. This observation would be expected since cobalt (ii) chloride hexahydrate is only red when in solution and when it is present as a compound or solid it is colorless. So, as the paper dries, the water where the salt is dissolved is evaporated and what is left on the paper would be the salt only which would be colorless so we would expect that we cannot see any visible writings on the paper.