Option 1 states that only Monera has unicellular organisms. Monera is a kingdom that consists of organisms like bacteria and archaea. These organisms are typically unicellular, meaning they are made up of a single cell. Therefore, option 1 is correct.

Option 2 states that only Protista has unicellular organisms. Protista is a kingdom that includes a diverse group of organisms such as algae and protozoa. While many types of Protista are indeed unicellular, there are also multicellular organisms within this kingdom. Therefore, option 2 is incorrect.

Option 3 states that both Monera and Protista have unicellular organisms. As mentioned earlier, Monera comprises of unicellular organisms, and Protista also has both unicellular and multicellular organisms. Therefore, option 3 is correct.

Option 4 states that both Protista and fungi have unicellular organisms. This statement is incorrect. Fungi is a separate kingdom that consists of organisms such as mushrooms and yeasts. While fungi can have both unicellular and multicellular forms, it does not fit the criteria for this question, which is to identify the kingdoms that exclusively have unicellular organisms. Therefore, option 4 is incorrect.

In conclusion, the correct answer is option 3.