The correct option is 4.

To determine the total number of ions produced from the coordination compound [Cr(NH₃)₆]Cl₃ in an aqueous solution, we need to understand how coordination compounds dissociate in water.

Coordination compounds consist of a coordination sphere (written inside square brackets) and counter ions (written outside the square brackets). When dissolved in water, the bonds between the central metal ion and the ligands inside the coordination sphere are strong covalent/coordinate bonds, so the complex ion does not dissociate further. However, the ionic bonds between the complex cation and the counter anions dissociate completely.

The dissociation of [Cr(NH₃)₆]Cl₃ in an aqueous solution can be represented by the following chemical equation:

$$[\text{Cr}{({\text{NH}}_3)}_6]{\text{Cl}}_3(\text{aq})\to {[\text{Cr}{({\text{NH}}_3)}_6]}^{3+}(\text{aq})+3{\text{Cl}}^{-}(\text{aq})$$

From the equation, we can count the species generated in solution:
1. One complex cation: [Cr(NH₃)₆]³⁺
2. Three chloride anions: 3 Cl^-

Therefore, the total number of ions produced is 1 + 3 = 4.