How to use not equal to inside a Yii2 query

In this case you need to use operator format: [operator, operand1, operand2, ...]. So your code should look like this:

$details = MovieShows::find()
           ->where(['movie_id'=>$id])
           ->andWhere(['location_id'=>$loc_id])
           ->andWhere(['<>','cancel_date', $date])
           ->all();

More about using where method and operator format