Methylene blue, from its aqueous solution, is adsorbed on activated...

It is the process of Physical adsorption as charcoal is already activated.
Since physical adsorption is spontaneous $\Delta \text{G}$ is -ve
$\Delta \text{G} = \Delta \text{H} - \text{T} \Delta \text{S}$
as $\Delta \text{S}$ is -ve (passage of methylene blue from aqueous phase over the surface of adsorbent) i.e. $\Delta \text{H}$ is highly -ve since process is exothermic in nature.

Physical adsorption is reversible in nature.

Physical adsorption decreases with increase in temperature.