1. **Problem statement:** Find the number of license plates with 4 letters followed by 2 digits where no letters or digits are repeated. 2. **Formula and rules:** - Letters: 26 letters, no repetition, order matters, so permutations $P(26,4) = 26 \times 25 \times 24 \times 23$ - Digits: 10 digits, no repetition, order matters, so permutations $P(10,2) = 10 \times 9$ 3. **Calculate total number of license plates with no repetition:** $$ P(26,4) \times P(10,2) = (26 \times 25 \times 24 \times 23) \times (10 \times 9) $$ 4. **Intermediate calculation:** $$ 26 \times 25 = 650 $$ $$ 650 \times 24 = 15600 $$ $$ 15600 \times 23 = 358800 $$ $$ 10 \times 9 = 90 $$ 5. **Final calculation:** $$ 358800 \times 90 = 32392000 $$ 6. **Answer:** There are $32392000$ license plates possible with no repeated letters or digits.