Learn Finnish: Hän antoi mekon räätälille helmikuussa. - She gave the dress to the tailor in February.

Because the action of giving is fully completed and she gave the whole dress. This requires the total object case, which for a singular noun looks identical to the genitive and ends in -n. If the action was somehow incomplete or ongoing, you would use the partitive mekkoa.

Why is the double kk from the dictionary word mekko reduced to a single k in mekon?

This is due to consonant gradation. Adding the -n ending closes the final syllable of the word. A closed syllable forces a strong consonant combination like kk to weaken into a single k.

Why is "to the tailor" translated with the allative case räätälille?

Verbs of giving and transferring, like antaa, require the recipient to be in the allative case (ending in -lle, which literally means "onto"). In Finnish grammar, you give something "onto" a person.

Why does "in February" use the inessive case (helmikuussa)?

In Finnish time expressions, months always take the inessive case (ending in -ssa or -ssä, literally "inside"). This is a set rule you can contrast with days of the week, which take the essive case instead (like maanantaina).