Acertain insulation has a thermal conductivity of 0.2 w/m °c what thickness is necessary to effect a temperature drop of 400°c for a heat flux of 200 w/m2?

It is necessary 1 meter of thickness.

Explanation:

You need to know the equation (P/A)=(k*T)/(L), where P/A is the heat flux, k is the thermal conductivity, T the temperature drop, and L the unknown thickness. So if rearrange the variables you will have that L = (k*T)/(P/A), and substituting the terms L = (0.2*400)/(200) = 1 meter