I tried this input, hoping to see returned x=7 as a solution:
solve PrimeQ(x-2) || PrimeQ(x-6)) for x<10
Result returned was: False x<10
How might I reform this to see the result I seek?
Yes, that is better, I really appreciate it.
Try
Select[Range[9],PrimeQ[#-2]||PrimeQ[#-6]&]
and see how WolframAlpha interprets that.
That is using a couple of Mathematica functions that WolframAlpha seems to understand and translates into WolframAlpha notation.