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In this scenario, the measurement of 2mg of Haldol solution requires precision, as accuracy is critical when administering medication to prevent potential risks or adverse effects. The appropriate device for accurately measuring such a small dosage of liquid medication is typically a syringe. Syringes are designed for dosing small quantities of liquid and allow for precise measurement in milliliters or other small increments.

Medication cups and teaspoons are not suitable for measuring small dosages like 2mg of Haldol solution. Medication cups may not provide the same level of accuracy due to their design, which is typically used for larger volumes. Similarly, teaspoons are not standardized for medical dosing and can lead to inaccuracies in measurement. Given these considerations, it is clear that a syringe would be the correct choice for administering this specific dosage of medication.