Final answer:
The invalid StringBuilder constructor, given the declarations, is 'buf = new StringBuilder(buf2, 32);' as there is no constructor taking a StringBuilder and an integer.
Step-by-step explanation:
The student has asked about which option is not a valid StringBuilder constructor following the given declarations. In Java, the StringBuilder class has several constructors, but the declaration buf = new StringBuilder(buf2, 32); is not valid as there is no constructor that takes a StringBuilder object and an integer as parameters. The valid constructors are a. buf = new StringBuilder(); which creates a new StringBuilder with no characters in it and an initial capacity of 16 characters, c. buf = new StringBuilder(32); which creates a new StringBuilder with no characters and a specified capacity of 32 characters, and d. buf = new StringBuilder(c); which creates a new StringBuilder that contains the same characters as the specified string.