How to solve this problem using supermesh analysis
Mesh Solution
Mesh analysis entails identifying each of the loops in a circuit and the voltage drops in those loops per Kirchoff's Voltage Law. A single current flows in the loop, and relates to the voltage drops of interest by Ohm's Law. Notice that a current (and therefore current source) is not required to use KVL, it is just related to KVL by Ohm's Law.
Here, it is easy to identify the loop on the left. There are also two independent loops on the right, which may be combined to make the right side into a supermesh loop; 'super' generally indicates that two smaller parts are combined into a larger one. Then, the Voltage-Controlled Voltage Source relates the two loops.
Let me know if I have clarified what is meant by mesh and supermesh analysis, and I will return to this in a short while when I have time to show what I mean with a solution to the problem using mesh analysis.
Simpler Calculations
As for whether this is easier, I think that mesh analysis is very close to circuit fundamentals and is easy to understand. In terms of calculation efficiency, it is fastest to recognise the left loop as a voltage divider, combine the series resistors in the right loop, use current divider equations, then Ohm's Law on the resistor across the output to obtain the voltage. I will show this with a second solution.
Voltage divider:
\$V_P=1000/(1000+50)\$
Current divider:
\$I_o=40V_P*50000/(50000+5100)=40(1000/1050)(50000/55100)=34.569A\$
\$V_o=-I_o*R=-34.569*5000=-172.8kV\$
note the negative polarity of the voltage due to the direction of the current through the output resistor