In this question, we are given the word "INTELLIGENCE" and we need to identify the word that cannot be formed using the letters in this word.
Option 1: ENTICE
The letters in "ENTICE" can be found in "INTELLIGENCE", so this option is incorrect.
Option 2: GENTLE
The letters in "GENTLE" can also be found in "INTELLIGENCE", so this option is incorrect.
Option 3: ENGINE
The letters in "ENGINE" can also be found in "INTELLIGENCE", so this option is incorrect.
Option 4: INTENT
The letters in "INTENT" can be found in "INTELLIGENCE", so this option is incorrect.
Therefore, the correct answer is option 4 since none of the other options satisfy the condition of not being able to form a word using the letters in "INTELLIGENCE".