Ben arkadaşlarımla fotoğraf paylaşabilmek için interneti kullanıyorum.

The suffix –ebilmek adds the meaning “to be able to.”

• paylaşmak = “to share”
• paylaşabilmek = “to be able to share”
  Here the speaker emphasizes ability or possibility: “I use the Internet so that I can share photos.”

Two things are happening: possession and the comitative case.

1. arkadaşlar = “friends”
2. arkadaşlar-ım = “my friends” (-ım marks 1st-person-singular possession)
3. arkadaşlarımla = “with my friends” (the ending -la means “with”)
   So arkadaşlarımla literally means “with my friends.”

Turkish marks a definite direct object with the accusative suffix.

• internet (no suffix) would be an indefinite object (“some Internet,” which is odd)
• interneti (-i) indicates “the Internet” as a specific thing you are using.
  Thus interneti kullanıyorum = “I am using the Internet” (definitely, not “some Internet”).

için means “for” or “in order to.” Here it introduces a purpose clause.

• fotoğraf paylaşabilmek için = “in order to be able to share photos”
  It explains why you are using the Internet.

In Turkish subject pronouns are optional because the verb ending (-yor-um) already indicates 1st person singular.

• kullanıyorum = “I use” or “I am using”
  Adding Ben can add emphasis (“As for me, I use the Internet…”) or clarity in longer sentences.

Turkish is typically Subject-Object-Verb (SOV). All modifiers and objects precede the main verb.

• Ben (S)
• arkadaşlarımla fotoğraf paylaşabilmek için interneti (O + purpose phrase)
• kullanıyorum (V)
  This order is normal in Turkish.

In non-finite (infinitive) clauses, objects are usually left unmarked if they’re indefinite.

• fotoğraf paylaşmak için = “to share (some) photos” (indefinite object)
  If you wanted “to share the photo,” you could say fotoğrafı paylaşabilmek için. Here it’s general “photos,” so no suffix is needed.