I ready for confirmations from a transaction from one other particular person.

If the transaction is “from one other particular person” that usually means they’re sending cash and you’re the recipient. They create the transaction not you.

“The Transaction is just accessible in your native machine.”

That message solely seems if you create a transaction.

I deleted it. Will I nonetheless acquired the bitcoins?

You, as a recipient, can not delete transactions created by another person.

You deleting a transaction you created can not have an effect on a unique transaction which another person created to ship you cash.

The type of confusion obvious on this query makes me suspect that you simply is likely to be new to Bitcoin and is likely to be being tricked by a felony, a confidence trickster.