> Og nú leitar hann ráðs með þeim hætti að hann bað konur bera út

búnyt að þeim

You could maybe paraphrase it as something like "and now he tries to
resolve the situation by asking the women to carry milk out to them"
or, straying slightly less from the original idiom, "and now he
attempts the following plan: he asked the women to carry milk out to
them".

Literally, "And now he tries a plan [seeks/attemts (useful/good)
course of action] in this way/manner, [namely] that he asked [the]
women to carry milk out to them".

'hætti' is dative singular of 'hátt(u)r' "way, manner".