Your grandfather works on the new york times crossword puzzle every day. he has been very good at solving the puzzle and nearly always does. his ability to remember the meaning of words has shown no decline as he has aged, and really shows very little decline for most older adults. what type of memory is this?

This is semantic memory.
Semantic memory actually refers to your 'general knowledge' - the information that you know about the world in general. The grandfather's semantic memory is quite strong and it doesn't seem to decline, which is why he is still so good at solving crossword puzzles. This refers to knowledge and memory that we accumulate throughout our lives.