"I wasn't able to keep this secret, and I'm ashamed of it."

Translation: Je n'ai pas pu garder ce secret et j'en ai honte.

[George583678]

I translated wasn't as the imperfect but was marked wrong.

[TimmyKilminster]

I would think the imperfect suggests you were a complete blabbermouth whereas the perfect confines your indiscretion to a single - embarrassing - incident.

[Sitesurf]

That's correct.

[deactivated user]

Duo has just let me know that my suggested translation has been accepted: “Je ne pouvais pas garder ce secret et j'en ai honte ”

[-BigWayne19-]

------ also: je n'etais pas capable de garder ce secret et j'en ai honte

[GraemeSarg]

I think that's what the English sentence means.

A single event would be "I couldn't keep this secret …" or "I haven't been able to keep this secret …".

"I wasn't able to" = "I was unable" and I think "I was" corresponds to imparfait, "j'étais" not "j'ai été".

[Poef9]

Is there also a correct solution involving "n'arriver pas à" ?

[Sitesurf]

Not on the list of accepted answers but in real life, you could say "Je ne suis pas arrivé(e) à garder ce secret..."

[effyleven]

Oh, poo! I missed out "pu." (wordbank)

[Seenoff]

This is a typical french curve ball. The English translation "I'm ashamed...." is clearly present tense, but the french use the past tense (smoke and mirrors ?)

[lulularosa]

Not smoke and mirrors, just a misreading on your part.
honte is a noun meaning "shame", not the past participle of a verb.
The word-for-word translation of J'ai honte is "I have shame" and the usual way of saying it in English is "I am ashamed".