Step 1: Spot the key clues:
The words livestock, grazing ground, seasonal cycle, lowlands and highlands all point to pastoral life and not to farming.
Step 2: Separate farming terms from herding terms:
Jhuming and the swidden method are both names for slash and burn cultivation. They deal with fields and crops, so we can remove options 1 and 4 together.
Step 3: Separate the general from the specific:
Animal husbandry covers all rearing of animals, including stall feeding with no travel at all. The question needs the specific practice of moving between two pastures with the seasons, so option 3 is too general.
Step 4: Choose the match:
The specific word for this seasonal up and down movement of herds is transhumance, which is option 2.
Step 5: Example to fix the idea:
Bakarwal herders of Jammu and Kashmir take sheep and goats to high meadows in summer and bring them back to the plains in winter. This yearly cycle is exactly what the question describes.
Final Answer:
The term that fits the description is transhumance, option 2.
\[ \boxed{\text{Option 2}} \]