Question

How did lord dalhousie and lord canning humiliate the mughal emperor?

Answer 1

Hello Dear.
Your answer is here 
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⇒ Lord Dalhousie was the governor general of India in the year 1846-56. 
⇒ Lord Dalhousie Introduces the Doctrine of Lapse policy which enables him to annex vast territory of India , Like- Jhansi , Satara, Nagpur, etc. 

⇒ Lord Dalhousie declared that after the death of Bahadur Shah Zafar, The emperor & successor would have to leave the royal palace , i.e the Red Fort.  
⇒ Later Lord Canning , The next governor General after the Lord Dalhousie announce in 1856 A.D.  that Bahadur Shah's successor wouldn't be allowed even to use the title of a king' . Similarly , the regal title of Nawabs of Carnatic & Nawabs of Tanjore were abolished . Such discourtesies were resented by the people & the Indian Rulers.
⇒ This become the one of the Major political cause of the Revolt of 1857.

Lord Dalhousie & Lord Canning Annex these states because of the following reasons-
1)→ To Expand the British Empire
2)→ To rule over India for a Longer Time or to Keep Themselves in Power.
3)→To further exploits & carry it's wealth to England 
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I anticipate it helps you. :-) 
Have a Marvelous Day.

Answer 2

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• lord dalhousie announced that on death of the king his successor would have to leave the imperial palace( the red fort). later, lord canning made it known that bahadur shah's successor would not be allowed to use imperial title. this is how lord dalhousie and lord canning smacked of discourtesy to the mughal emperor.