The term 'PREFIX WITH SCIENCE OR INTELLECTUAL' can be solved by the word 'PSEUDO, ' which is a six-letter prefix meaning FALSE or fake. It is derived from the Greek word 'pseudes, ' meaning 'LYING' or 'FALSE.' This prefix is often used to describe something that appears to be real but is actually FALSE or not genuine. It is commonly used in scientific and intellectual contexts, such as in the words 'pseudoscience' and 'pseudointellectual.'