Question 4396
My obligatory cartoon: 

{{{
cartoon( 
  log( 4, (x-2) )+log(4, (x-8) )= 2,
  4^(log( 4, (x-2) )+log(4, (x-8) ))= 4^2,
  (4^log( 4, (x-2) )) * (4^log(4, (x-8) ))= 4^2,
  (x-2)*(x-8) = 4^2 = 16
)
}}}

Exponentiate both sides, that is, take 4 to the power of both sides:

{{{log( 4, (x-2) )+log(4, (x-8) )= 2}}}


{{{4^(log( 4, (x-2) )+log(4, (x-8) ))= 4^2}}}


{{{(4^log( 4, (x-2) )) * (4^log(4, (x-8) ))= 4^2}}}


Note that {{{a^log(a, b) = b}}}, so {{{4^log( 4, (x-2) ) = x-2}}}.


{{{(x-2)*(x-8) = 4^2 = 16}}}

{{{(x-2)*(x-8) = 16}}}

that simplifies to a simple quadratic equation, solve it. x=10 is one obvious answer, there could be another.