See explanation.
I am not sure why the answer is missing a very essential point which is teaching the student Le Chtelier’s principle . Maybe this is not a grade 12 question!!!!
The student could easily deduce that since the ##[I_2]=0M## the equilibrium will shift toward the direction of making ##I_2## and therefore to the left and in this case the ICE table is written as follows:
## H_2(g)+I_2(g)rightleftharpoons 2HI(g)##
##Initial 8M 0M 2.4M##
##Change +x +x -2x##
##Equilibrium 8+x x 2.4-2x ##
In this case ONLY ##color(green)(positive)## values of ##x## will be accepted.
However the way the answer is written is that he will assume that the equilibrium is shifting to the right and in this case ##x## will be ##color(green)(positive)## however if his assumption is wrong ##x## will be ##color(red)(negative)## and this is the case that is why the ##[HI]## dropped from ##2.4M## to ##2.2M##.