The verb regarder means "to look at" or "to watch." It implies a deliberate, sustained act of directing one's eyes at something, as opposed to voir (to see), which refers to passive perception.
Among the options, observer longuement (to observe at length) best captures this meaning. Regarder involves intentionality and attention - when you regardez something, you are actively focusing on it, much like observing it carefully.
The other options do not match:
ignorer means "to ignore" - the opposite of paying attention to something.
demander means "to ask" - an entirely unrelated action.
voir brievement means "to see briefly" - this is closer to apercevoir (to catch a glimpse of), which is the opposite of sustained, deliberate looking.
The key distinction to remember: regarder = active, intentional looking; voir = passive, incidental seeing.
