The largest 4-digit number formed by 6,7,0,9 using each once is 9760.
Step 1: We must make a 4-digit number using the digits 6, 7, 0, 9 — each only once.
Step 2: In a 4-digit number, the thousands place cannot be 0.
Step 3: To get the largest number, put the biggest non-zero digit in the thousands place:
\(\text{Thousands place} = 9\)
Step 4: The remaining digits are 7, 6, and 0. To keep the number as large as possible, put the next biggest in the hundreds place, then the next in the tens place:
\(\text{Hundreds place} = 7\)
\(\text{Tens place} = 6\)
Step 5: Put 0 in the units place (this makes the least impact on the value):
\(\text{Units place} = 0\)
Step 6: The number formed is:
\(9\,760\)
Step 7 (Quick check): We used each digit once, it is 4 digits, and any other place for 0 makes it smaller, e.g.
\(9\,706 < 9\,760\) and \(9\,670 < 9\,760\).
Conclusion: The statement is true.