In demo 6 the header style is "transparent" and the course layout is "c2", so go to wp-admin->appearance->customize->layouts->course layout and set it to "c2" and save changes.
You can refer this tip:
https://wplms.io/support/knowledge-base/one-click-setup-wplms-demo1/
But it for fresh install only, so might want to refer this tip:
https://wplms.io/support/knowledge-base/installing-demo-1-without-sample-data/
It is for demo1 but you can use it with demo 6, and only import the customiser.txt file because you don't want to change the homepage.
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This will not change the website exactly like demo 6 because modern child theme is for some specific design and it overrides the default template, but it will change the color settings layout setting, etc according to demo 6.