First, rewrite we can expand the expression by multiplying each term in parenthesis by the term outside the parenthesis:
#sqrt(color(red)(2x))(sqrt(color(blue)(8x)) - sqrt(color(blue)(32))) =>#
#(sqrt(color(red)(2x)) * sqrt(color(blue)(8x))) - (sqrt(color(red)(2x)) * sqrt(color(blue)(32)))#
We can next use this rule for radicals to execute the two multiplication operations:
#sqrt(color(red)(a)) * sqrt(color(blue)(b)) = sqrt(color(red)(a) * color(blue)(b))#
#(sqrt(color(red)(2x)) * sqrt(color(blue)(8x))) - (sqrt(color(red)(2x)) * sqrt(color(blue)(32))) =>#
#sqrt(color(red)(2x) * color(blue)(8x)) - sqrt(color(red)(2x) * color(blue)(32)) =>#
#sqrt(16x^2) - sqrt(64x) =>#
#4x - sqrt(color(red)(64) * color(blue)(x)) =>#
#4x - (sqrt(color(red)(64)) * sqrt(color(blue)(x))) =>#
#4x - 8sqrt(x)#