how exactly does solving nounce verify the transaction How exactly does solving nounce verify the transaction. or how are both of them interrelated.how does my transaction gets verified.
Simply, it doesn't. The hashing puzzle is only needed for all nodes to agree on a common value. Once a block is found it is propagated through the network.
If the nounce is valid AND if the transactions in the blocks are valid then the block is accepted into the blockchain.
A transaction is valid if:


each transaction input matches a previous transaction output.
they are reedemed by their legitimate owners
the sum of values of all transaction outputs is less than or equal to the sum of the values of all inputs.


This verification is performed by bitcoin nodes. A miner is not incentivized to include invalid transactions in their blocks as they will invalidate the entire block (thus preventing the miners to obtain the coinbase reward).