To solve this problem, we can use a proportion:
(2.0 mg) / (x mL) = (30 mg) / (6.0 mL)
where x is the unknown number of milliliters we need to administer.
To solve for x, we can cross-multiply and simplify:
(2.0 mg) * (6.0 mL) = (30 mg) * (x mL)
12 = 30x
x = 12/30 = 0.4 mL
Therefore, we should administer 0.4 mL of morphine to the patient.