Apostrophe is used before 's' to indicate possession of singular subject. Apostrophe is used after 's' to indicate possession of plural subject that end in 's' (E.g., cats - cats'). Here, the subject 'Charles' is singular. However, there are two ways in which possession is indicated for nouns ending in 's': adding an apostrophe at the end alone and adding 's at the end of the noun. Therefore, the correct options are: Charles' daughter as well as Charles's daughter. You may think only one of them is right, however, both are acceptable in modern-day English, but the apostrophe after the 's' is more commonly used in case of plural nouns.