Final answer:
The best replacement for 'launder' in the sentence is 'wash' (option c), as it describes the action of cleaning the shirt, which matches the original intent of the word 'launder'.
Step-by-step explanation:
The best replacement for the underlined word 'launder' in the sentence "my mother needs to launder my shirt as it is dirty" is c. wash. The word 'launder' specifically means to wash or clean, especially clothes and linens. Therefore, the word 'wash' directly corresponds to the original meaning intended in the sentence.
Option (a) 'wear' is not suitable since it refers to putting on clothes, not cleaning them. Option (b) 'hang' is also incorrect because it usually refers to placing clothes on a hanger or line, generally after they have been washed. Option (d) 'dry' is also not a correct replacement, as it relates to removing moisture from clothes, usually after they have been washed.
When replacing words, it is vital to consider the context and synonyms that could match the original word's intent. In our case, if the shirt is dirty and needs to be cleaned, 'wash' is the operation we're describing, thus making it the ideal synonym for 'launder'.