documentclass[12pt,a4paper]{book}
usepackage{enumitem,calc}
setlist[enumerate]{labelsep=10pt,leftmargin=45pt}
setlist[enumerate,1]{label= $arabic*.$}
setlist[enumerate,2]{leftmargin=*,label=theenumi$arabic*$),ref=theenumi$arabic*$}
usepackage{amsmath,amsthm,amssymb}
newtheorem{exer}{Exercise}[section]
usepackage{answers}
Newassociation{solution}{Solution}{ans}
renewcommand{Solutionlabel}[1]{#1}
usepackage{multicol}
begin{document}
Opensolutionfile{ans}[exer1.1]
begin{exer}label{exer1.1}mbox{ }
begin{enumerate}
    item First problem
    begin{solution}
    Sol. of first problem
    end{solution}
    item Second problem
begin{enumerate}
begin{multicols}{2}
    item Sub second problem
    begin{solution}
        Sol. of 2.1
    end{solution}
    item Sub second problem
    begin{solution}
        Sol. of 2.2
    end{solution}
    item Sub second problem
    begin{solution}
        Sol. of 2.3
    end{solution}
    item Sub second problem
    begin{solution}
        Sol. of 2.4
    end{solution}
end{multicols}
end{enumerate}
end{enumerate}
end{exer}
Closesolutionfile{ans}

bigskip

section*{centering Solutions of Chapter thechapter}

subsection*{Solutions of Exercise ref{exer1.1}}
input{exer1.1}
end{document}