"The women walk to the store and chat."
Translation:A nők elsétálnak az üzletbe és beszélgetnek.
"mennek" = "they go". So it's not specifically walk.
it's hard to say general rules for suffixes like "el"
But "ELmenni" is an idiomatic expression. It's generally used when you are planning to go somewhere, without having started the journey, and you are informing someone that you will go.
"Elmegyek a boltba" = "I'm going to the store" -- You are at home, saying to someone that you're going to the store.
"Megyek a boltba" is okay here too, but "elmegyek" is more idiomatic.
If you are already on your way and someone calls you, asking what you are doing, then you would say "(Éppen) megyek a boltba" = "I'm going to the store (at the moment)"
using "elmegyek" would be wrong here.
Same logic applies for "sétálni" but I wanted to show it with "menni" because it's much more common.
A nők sétálnak az üzlethez és beszélgetnek. Not accepted, reported. I can see that, maybe, elsétálnak, would have been better but if we're simply saying that they're walking, (see the logic of pythagoras322 on this), sétálnak should be OK. Otherwise, üzlethez must be just as valid as üzletbe. We don't know if they're both going into the store but they're certainly going to the store because the question says so.
In fact, I now see what I wrote 2 months ago so üzlethez doesn't seem to be the problem. It was the missing "el" because I put the verb before the destination. Is it wrong to miss the "el?"