The two leadership styles combined have a demonstrable effect on team effectiveness
or
The two leadership styles combined has a demonstrable effect on team effectiveness
Replacing "the two leadership styles" with the plural "they", you could rephrase the sentence as:
"Combined, they have a demonstrable effect on team effectiveness."
The word "has" is used with a third singular person (he/she/it or a noun), and "have" is used in all other cases. Since "the two leadership styles" is not singular, the entire phrase must be followed by "have".
A complete list of the conjugation for the verb is here.
I think the answer would be the first one
The two leadership styles combined have a demonstrable effect on team effectiveness
The sentence above is about style, the subject leadarship styles
.
Anyone can easily get confused with the words following the subjects ie. combined
or any of these merged, mixed, together
. Even-if it still conveys the idea that some multiple subjects are combined into one, the verb agreement should always be plural.
That's what I think and I will be glad if anyone makes me correct.