Learn Russian: По-моему, они послали Анну за аптечкой. - In my opinion, they sent Anna for the first aid kit.

When за is followed by the instrumental case, it expresses the purpose of an action meant to fetch, retrieve, or bring something back. If we used the accusative case here (за аптечку), it would mean they sent Anna to physically stand or look behind the first aid kit.

How does the word 'аптечка' (first aid kit) relate to the word for pharmacy?

аптечка is derived from аптека (pharmacy). By adding a diminutive suffix, which causes a consonant mutation from 'к' to 'ч', Russian creates a word that essentially translates to a 'little pharmacy'.

Could we use the imperfective verb 'посылали' here instead?

In this specific context, you need the perfective послали because it describes a single, completed action with a specific result. Using the imperfective посылали would change the meaning to a repeated action (they used to send her) or just the general process of sending someone.

Why is there a hyphen in 'По-моему' and a comma right after it?

Adverbs formed with the prefix по- and ending in -ому or -ему (like по-моему, по-твоему) are always hyphenated. The comma is required because the word acts as a parenthetical or introductory phrase expressing an opinion, much like setting off 'In my opinion' with a comma in English.