As a verb form, in past and perfect tenses, both are correct. You can say either 'He burned his hand' or 'He burnt his hand'. When the past participle is used as an adjective we can only use 'burnt', for example 'He likes to eat burnt toast'.

Both are correct. The past tense of some verbs can end in both -ed and -nt For example: lear-learned/learnt burn - burned/burnt Other verbs that follow this rule: dream, dwell, smell, spill, spoil. The ed form is preferred in American English (AmE) whereas the nt form is more common in British English (BrE).