Since the triangle is equilateral, then all the sides have the same length. Then:
[tex]12x-4=6x+8[/tex]
Solve for x:
[tex]\begin{gathered} \Rightarrow12x-6x=8+4 \\ \Rightarrow6x=12 \\ \Rightarrow x=\frac{12}{6} \\ \therefore x=2 \end{gathered}[/tex]
Substitute x=2 in any of the expressions for the length of a side to find the measure of the side of the triangle:
[tex]6(2)+8=12+8=20[/tex]
Since one side has a length of 20 and the triangle has three equal-length sides, then the perimeter is:
[tex]\begin{gathered} P=3\cdot20 \\ =60 \end{gathered}[/tex]
Therefore, the perimeter of the equilateral triangle is 60.
