The perimeter is the sum of all sides.
[tex]2(3x-2)+3(2x+4)=104 \\
6x-4+6x+12=104 \\
12x+8=104 \ \ \ |-8 \\
12x=96 \ \ \ |\div 12 \\
x=8 \\ \\
3x-2=3 \times 8-2=24-2=22 \\ \\
2x+4=2 \times 8+4=16+4=20[/tex]
Two sides have a length of 22 cm, three sides have a length of 20 cm.
The longest side is 22 cm long.