"The house has no electrical sockets."
Translation:Das Haus hat keine Steckdosen.
The ending of kein- is like the ending of ein-. You need to modify it according to the characteristics of the noun (its case and gender, including whether it is plural or not). Here we have an example where the noun is plural, in accusative case. The ending you need for this is -e, so we get keine.
Here are some other examples:
Das ist kein Käse - masculine, nominative case
Sie hat keinen Stift - masculine, accusative case
Er mag keine Blume - feminine, accusative case
Es gibt heute keine Filme - plural, accusative case
You can find the declension tables on Wikipedia, if you haven't copied them into your own notes already.
That's a grammatically correct sentence, but it's not a good translation of Duo's English sentence.
It would be better as a translation of "The house has no socket" or "The house does not have a socket".
Your use of the singular keine Steckdose implies that if it did have a socket, it would have exactly one.
But since houses usually have many sockets, the plural keine Steckdosen makes more sense.
I did the same thing. In Romance languages, when you say something doesn't have something, you have to say it has nothing, not even one. So you use the singular.
When the subject is displaced from the initial position, it generally comes right after the verb, so you would have Steckdosen hat das Haus... and then the rest of the sentence -- which in this case is just the word keine.
Steckdosen hat das Haus keine is a slightly unusual ordering, though. It topicalises Steckdosen -- "As for sockets: the house has none of those."
Steckdosen hat das Haus keine (with capitalised Haus) is a grammatically correct sentence.