Question 992206
Your perimeter seems to mean, for both triangles together.


Not clear is, which part of either triangle is to be shortest side of 4 units.  Taking the longer side as x, then the perimeter sum is  2(4+2x).  


{{{2(2x+4)=6*4}}}


{{{4x+8=24}}}
{{{x+2=6}}}
{{{x=4}}}, but this would be equilateral, NOT isosceles.


The other possibility is that x should be the either of the equal side. The sum of perimeters would be  {{{2(x+2*4)}}}, and then the perimeter relationship would become  {{{2(x+2*4)=6*4}}}, six times the length of the shortest side of 4.
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{{{2x+16=24}}}
{{{x+8=12}}}
{{{x=4}}}, still not what you want, still being equilateral.


Did you maybe have a mistake in the description?