isn't thevenin equivilant the same circuit as the original why is my Power different?

So I am doing maximum average power transfer and my answer is off from the solution given. So basically the solution made a thevenin eq circuit then connect that to the R_load to find the V_load. while I connected the R_L to the original circuit to find the V_L. technically from what I know it shouldn't make a differences but my answer and the solution seems to be off by too much so I am hoping if anyone can point out if it is the same or is there somethting wrong with my idea/method. The black and while second picture is the provided solution while the bottom one is my workings.

https://preview.redd.it/hidlnvp2g04e1.png?width=1907&format=png&auto=webp&s=461e2c908ff82215810f8de6f25281d39a13e0d7

https://preview.redd.it/rf9hn5h6g04e1.png?width=715&format=png&auto=webp&s=e76264cc911cd3a05bcf2aa79e8484b9e5389cc6

https://preview.redd.it/lne3c30gg04e1.png?width=812&format=png&auto=webp&s=a2c203b7669ee87671561a23e4fa54348c785d69