Hyphenated words are complicated and depend on which style you are using.
Using The Chicago Manual of Style:
- Always capitalize the first element.
- Capitalize any subsequent elements unless they are articles, prepositions, coordinating conjunctions
- If the first element is merely a prefix or combining form that could not stand by itself as a word (anti, pre, etc.), do not capitalize the second element unless it is a proper noun or proper adjective.
- Capitalize the second element in a hyphenated spelled-out number (twenty-one or twenty-first, etc.) or hyphenated simple fraction (two-thirds in two-thirds majority).
- Capitalize the first and second element of a hyphenated phrase