I agree. To give has to have both a direct object and and indirect object. However, in context the IO could be implied. Like deciding who's giving what (to someone) from a list. But it would be better here, where there's no context, to include it. We also need to know how to express it. Like Θα σου δώσω το κινητό.
In English we dont use "cellphone" we say 'mobile'. But given Duolingo uses an American flag icon to denote teaching English, and uses only American spellings of English words, this is not a surprising feature.
It must be confusing for those wanting to learn English instead of American!