Learn Russian: Я могу часами любоваться этой картиной.

In Russian, putting a time noun in the plural instrumental case emphasizes a long, continuous duration or a repeated action. So часами essentially means "by the hours" and translates to "for hours." You will also see this pattern with other time words, like годами (for years) or вечерами (evenings).

Why is этой картиной in the instrumental case?

It is required by the verb любоваться (to admire). Unlike the English verb "admire," which takes a direct object, любоваться requires the object you are admiring to be in the instrumental case. Since картина is a feminine noun, it becomes этой картиной.

Could I use смотреть на эту картину instead of любоваться этой картиной?

Grammatically yes, but the meaning changes slightly. Смотреть на simply means "to look at." Любоваться specifically means "to look at with pleasure" or "to admire." Using любоваться emphasizes the aesthetic enjoyment you are getting from the painting.