documentclass{article}

usepackage{amsthm}
usepackage{chngcntr}
counterwithin*{equation}{section}
counterwithin*{equation}{subsection}
theoremstyle{remark}
newtheorem{problem}{Problem}

begin{document}


section{One}
begin{problem}
begin{equation}
f(x)=g(y)
end{equation}
begin{equation}
h(x)=p(z)
end{equation}
end{problem}

begin{equation}
h(x)=p(z)
end{equation}

section{Two}


begin{equation}
int f(x)dx=  int g(x)dx
end{equation}
begin{equation}
v=frac{e}{t} end{equation}
begin{problem}
begin{equation}
f(x)=g(y)
end{equation}
begin{equation}
h(x)=p(z)
end{equation}
end{problem}

end{document}

newenvironment{problem}[2][Problem]{stepcounter{myproblemcnt}setcounter{myproblemcnt}{#2}begin{trivlist}
item[hskip labelsep {bfseries #1}hskip labelsep {bfseries #2.}]}{end{trivlist}}

makeatletter
renewcommand{theequation}{arabic{myproblemcnt}.arabic{equation}}
newcounter{myproblemcnt}
@addtoreset{equation}{myproblemcnt}
makeatother