Final answer:
The blood specimen should be collected from below the hematoma on the left arm to avoid contamination and due to edema in the right arm, which can interfere with blood collection.
Step-by-step explanation:
When collecting blood from a patient with a very edematous right arm and a large hematoma in the antecubital area of the left arm, the phlebotomist should collect the specimen from below the hematoma. Drawing blood from above the hematoma could lead to contamination of the blood sample with the cellular components of the hematoma. Additionally, the antecubital area of the right arm should be avoided due to the edema, which can also interfere with blood collection and potentially cause discomfort or complications for the patient. The correct venipuncture site is thus below the hematoma where the veins are unaffected by the injury and edema.