IPA: /ɪnˈdɛlɪkət/
KK: /ɪnˈdɛlɪkət/
The quality of being rude or lacking sensitivity; a lack of tact or delicacy in behavior or speech.
His indelicateness in addressing the issue offended many people in the room.
Indelicateness is formed from "in-" (meaning not) and "delicatus" (from Latin, meaning delicate or pleasing). The suffix "-ness" (meaning the state of being) indicates a quality. Thus, indelicateness refers to the state of not being delicate or lacking in tact.
Think of 'not' ('in-') being combined with 'delicate' ('delicatus') to remember that indelicateness means lacking delicacy or tact.