The first step is to find the mg/mL of dopamine.
If there are 52 mg / 26 mL, then there are 2 mg / 1 mL (just reduce the fraction).
If we are losing 10 mL / 1 hour, and there are 2 mg / mL, then the flow rate of dopamine mg / hour is 20.
You can also do this using dimensional analysis.

Just cross out the units that cancel in the numerator and denominator (mL in this case), and you're left with mg / hour. Then multiply the numerators and divide by the denominators. You get the same answer.