From the given alternative words, select the word which cannot be formed using the letters of the word INTELLIGENCE.

Introduction / Context:
Word-formation questions check whether you can mentally track the availability and frequency of letters in a base word. The twist is that you are allowed to use each letter only as many times as it appears in the original word. Here, the base word is INTELLIGENCE, and you must decide which option cannot be formed from its letters under this restriction.

Given Data / Assumptions:
- Base word: INTELLIGENCE.
- Available letters and their counts are fixed by this word.
- Each letter can be used at most as many times as it appears in INTELLIGENCE.
- Option words: CANCEL, NEGLECT, GENTLE, INCITE.

Concept / Approach:
The core idea is to count letters. First, list the letters in the base word with their frequencies. Then, for each option word, compare the required letters and their counts with what is available. If any option demands a letter that either does not appear at all or appears more times than available, that word cannot be formed. Exactly one such option should fail this test.

Step-by-Step Solution:
Step 1: Write the base word INTELLIGENCE and count each letter. Letters: I, N, T, E, L, L, I, G, E, N, C, E. Frequencies: I(2), N(2), T(1), E(3), L(2), G(1), C(1). Step 2: Check CANCEL: C, A, N, C, E, L. It uses C twice and A once. INTELLIGENCE has only one C and no A at all, so CANCEL cannot be formed. Step 3: Check NEGLECT: N, E, G, L, E, C, T. Needed: N(1), E(2), G(1), L(1), C(1), T(1). All of these counts are within the available limits, so NEGLECT can be formed. Step 4: Check GENTLE: G, E, N, T, L, E. Needed: G(1), E(2), N(1), T(1), L(1). All are present in sufficient quantity, so GENTLE can be formed. Step 5: Check INCITE: I, N, C, I, T, E. Needed: I(2), N(1), C(1), T(1), E(1). Again, this is within the available counts, so INCITE can be formed.

Verification / Alternative check:
Summarise counts quickly: INTELLIGENCE has no A and only one C. CANCEL requires A and two Cs, which already violates the rules. The other three words use only letters present in INTELLIGENCE, and none of them exceed the available counts. So only CANCEL fails the formation test and is therefore the required answer.

Why Other Options Are Wrong:
- NEGLECT: all required letters occur in INTELLIGENCE, and each is used within limit.
- GENTLE: uses G, E, N, T, L, all of which are safely available.
- INCITE: uses I twice, N, C, T, E, and these frequencies all match or stay below the base word frequencies.

Common Pitfalls:
Students often check only whether letters exist, forgetting to check how many times they appear. Another common error is to miscount repeated letters like E or L in the base word. A systematic approach is to write the base letter frequencies clearly once, then tick off counts for each option word. This almost eliminates mistakes in such questions.

Final Answer:
The word that cannot be formed from INTELLIGENCE is CANCEL.