Answer: The answer is indeed letter B. The beach was full of happy, carefree tourists.
Step-by-step explanation:
One of the many uses of commas is to separate coordinate adjectives. Coordinate adjectives are words that come in a row and modify the same noun. In the sentence we are analyzing here, both "happy" and "carefree" are modifying the noun "tourists". Therefore, we must separate the adjectives with a comma - or use "and" between them, which is not the case here. Option B is, thus, the right one.
Option A brings a comma after the preposition "of", separating it from its object, which makes it incorrect.
Options C brings a comma after the second adjective, separating it from the noun it modifies. That also makes it an incorrect option.
Finally, option D brings a comma separating the subject and its verb, as well as a comma separating the preposition and its object. Again, it's an incorrect option.