To solve the mesh analysis problem, using a supermesh is recommended when dealing with circuits that include shared current sources. A supermesh is formed by combining the meshes that share a dependent or independent current source, allowing for the application of Kirchhoff's Voltage Law (KVL) across the entire loop. Additionally, Kirchhoff's Current Law (KCL) should be used to establish relationships between the currents involved, especially when no known voltage sources are present. For further assistance, network analysis tutorials are available online, which can provide additional guidance. Utilizing these techniques will aid in effectively analyzing the circuit.