R = d/(κ·A),
where the resistance is proportional to the thickness d of the material, and inversely proportional to the exposed surface area A and the material-dependent conductivity κ (lower-case Greek letter "kappa," in units of watts/m·K), which characterizes how well this material allows (or does not allow) heat to flow through it.
Rtotal = Rwall + Rbooks,
Rtotal = (dwall/(κwall·Awall)) + (dbooks/(κbooks·Abooks)),
where presumably the shared area A of the wall and the bookcase is the same value, but they have different d thicknesses and κ conductivities. The resulting power (heat flow per time) through the book layer and wall insulation is then:
Power = (heat flow)/time = ∆T/Rtotal.
In order to be consistent with all the other definitions of heat flow in this course, a negative sign must be put in to the version of the equation that is given in your textbook. Since a positive heat flow per time is energy being put into the object from the environment, this occurs if the temperature Tenv of the surrounding environment is greater than the object's temperature Tobj . A negative heat flow per time is energy being taken from the object out to the environment, so the temperature Tenv of the surrounding environment must be less than the object's Tobj temperature.