He wondered why the lights had been left on all night.

Explanation:

Step 1: Identify the tense in indirect speech

“He wondered why the lights had been left on all night.”

• Tense: Past Perfect Passive (had been left)

Step 2: Rule for changing to Direct Speech

When converting Indirect → Direct speech:

• Past Perfect → Simple Past
• “wondered” → “said”
• Question form is restored

Step 3: Apply the rule

👉 had been left (past perfect passive)
➡ becomes
👉 were left (simple past passive)

So the correct direct speech is:
“Why were the lights left on all night?”

❌ Why other options are wrong:

1. Why are the lights left…
   ❌ Present tense (incorrect)
2. Why have the lights been left…
   ❌ Present perfect (incorrect)
3. Why had the lights been left…
   ❌ Still in past perfect (no change made)

Extra Facts:

1. Tense Backshift Rule (Direct ↔ Indirect):
   • Present → Past
   • Past → Past Perfect
   • Past Perfect → Simple Past (when converting back)
2. “Wondered” is used for:
   • Indirect questions (no question mark)
   • Direct speech must restore question format
3. Passive remains passive during conversion
   • Only tense changes, not voice