Learn Hardcore Turkish: Harita üzerinde doğu ve batıyı çocuklara ben anlattım. - I explained east and west on the map to the children.

In coordinated objects, Turkish often attaches case only to the last item and lets it “spread” to the whole coordination. So doğu ve batıyı is understood as if it were doğuyu ve batıyı (“the east and the west” as a single definite object). Marking both is also fine and sometimes preferred for symmetry or clarity: doğuyu ve batıyı.

Is it wrong to say doğuyu ve batıyı instead?

Not at all—it's perfectly correct and very natural. Both doğu ve batıyı (case on the last conjunct) and doğuyu ve batıyı (case on both) are widely used.

Why is the accusative used here at all?

Turkish marks definite/specific direct objects with the accusative. Here, doğu ve batıyı are specific concepts being explained, so you get -(y)I. If you left the accusative off (e.g., doğu ve batı anlattım), it would sound like a non-specific, list-like object and is stylistically odd with anlatmak. With a non-specific reading, speakers more often switch verbs: e.g., doğu ve batıdan bahsettim (“I talked about east and west”).

What exactly is çocuklara doing, and how is it formed?

It’s the indirect object “to the children,” formed as plural + dative: çocuk-lar-a. Order of suffixes is plural first, then case. Singular would be çocuğa.

Do I need to say ben? The verb already shows “I”.

No, you don’t need it. Anlattım already encodes 1st person singular. Adding ben adds contrastive emphasis: “I (as opposed to someone else) explained it.”

Why is ben placed right before the verb?

In Turkish, the element immediately before the verb is the focus position. … ben anlattım emphasizes the subject: “It was me who explained it.” Other orders shift the focus:

Ben çocuklara… anlattım: neutral/subject topic.
Çocuklara ben anlattım: focus on “I,” with “to the children” as topic.
Ben anlattım çocuklara is possible but marked/stylistic; canonical focus is pre-verbal.

Can I say haritada instead of harita üzerinde?

Yes. Both mean “on the map.” Nuance:

haritada: everyday, compact.
harita üzerinde: more formal/technical, common in written or academic style.
haritanın üzerinde: very literal “on the surface of the map,” physical/locational.

Does harita üzerinde mean physically “on top of the map” or “by using the map”?

Context decides. In educational contexts it usually means “using the map as a medium.” If you need the strictly physical sense, haritanın üzerinde is the most literal.

Why is it batıyı with a y, and how would I write the form for doğu?

Turkish inserts a buffer consonant y when a vowel-final stem takes a vowel-initial suffix. So:

batı + -(y)ı → batıyı (last vowel ı → accusative -ı)
doğu + -(y)u → doğuyu (last vowel u → accusative -u) No apostrophes with common nouns: write batıyı, not batı’yı.

What’s going on in anlattım? Why the double t?

Root: anlat- (“to tell/explain”). Past tense suffix -DI voices/devoices to match the preceding consonant: after voiceless t, it becomes -tı. Then 1sg -m:

anlat- + -tı + -m → anlattım The doubled t is just the t at the end of the stem plus the t of the past suffix.

Should doğu and batı be capitalized?

Not here. Cardinal directions in general use are lowercase: doğu, batı. Capitalize when they are part of proper names or conventional regions: Doğu Anadolu, Uzak Doğu, Batı Avrupa.

Could I use öğrettim or açıkladım instead of anlattım?

anlatmak: to explain by telling/describing; very common in teaching contexts.
öğretmek: to teach (implies instruction/learning outcome). Doğu ve batıyı çocuklara öğrettim = “I taught the children east and west.”
açıklamak: to clarify/explicate (often more formal). … açıkladım is fine if you mean you clarified the concept.