#1#. Recall that you can add and subtract radicals if they have the same value in the square root sign. You can think of the #color(teal)("radical")# as a #color(teal)("variable")#. Thus, start by grouping all like terms together.
#color(red)2color(teal)(sqrt(3))# #color(orange)(-4)color(teal)(sqrt(2))# #color(blue)(+6)color(teal)(sqrt(3))# #color(purple)(+8)color(teal)(sqrt(2))#
#=color(red)2color(teal)(sqrt(3))# #color(blue)(+6)color(teal)(sqrt(3))# #color(orange)(-4)color(teal)(sqrt(2))# #color(purple)(+8)color(teal)(sqrt(2))#
#2#. Add/subtract as appropriate.
#=(color(red)2# #color(blue)(+6))color(teal)(sqrt(3))+(color(orange)(-4)# #color(purple)(+8))color(teal)(sqrt(2))#
#3#. Simplify.
#=color(green)(|bar(ul(color(white)(a/a)8sqrt(3)+4sqrt(2)color(white)(a/a)|)))#
