Learn Finnish: Sinun kannattaa oppia tämä kierre.

Normally, a total object takes the genitive-accusative case. However, this sentence is built around the necessity verb kannattaa (it is worthwhile). Necessity structures require a nominative object. Because the verb oppia (to learn) is chained to kannattaa, it inherits this rule. The whole chain acts as a necessity structure, leaving tämä kierre in the nominative.

Why is the subject Sinun in the genitive case rather than the nominative Sinä?

The verb kannattaa belongs to a special group of necessity verbs that require a genitive subject. Instead of the subject directly doing an action, the structure literally translates closer to 'Of you, it is worthwhile'. In these constructions, the person doing the action goes into the genitive case, and the main verb is locked in the third-person singular.

If the sentence were negative, how would the object case change?

If you negate the sentence to say you should not learn this spin (Sinun ei kannata oppia...), the object must change to the partitive case: tätä kierrettä. In Finnish, negative sentences always require a partitive object, which overrules the necessity structure's nominative object rule.

Could I use the partitive case tätä kierrettä in the positive sentence as well?