This may be a very basic question, but I don't know, so I'll ask. In the preceding image, why is it that the word is translated Yahweh if it's pronounced Yahovah (Jehovah)? I've seen both in Bibles, but are they different?
You mentioned that you didn't know why one of the offerings was accepted and another wasn't. Hopefully you weren't leaving your explanation for next week with the continuation of the passage. If so, don't read my thoughts here! :)
When it talks about Cain's offering, it says he brought an offering from the fruit of the ground. There are no qualifiers or descriptors on it. however, when it talks about Abel's offering, it says he brought from the firstborn of his flock, and that he brought from the fat of them. It sounds like Abel really brought the best of what he had, whereas (I as an English speaker would infer from the lack of adjectives that) Cain brought offerings that weren't the best of what he had.
God often doesn't look at what we do, but at why we do it. Later, when looking for someone to anoint king of Israel, God tells Samuel that "man looks at the outward appearance, but the Lord looks at the heart." We can possibly surmise that God saw that Abel strongly desired to honor God, and that he trusted God, but Cain was giving the offering as a technicality. I'm not sure, but that's my feeling.
What are your thoughts? Or is that something that you'll look at more this coming week?