\setupcaptions[
  way=bysection,
  prefixsegments=chapter:section,
]

\setupenumerations[
  way=bysection,
  prefix=yes,
  prefixsegments=chapter:section,
]

\defineenumeration[enumeration][text=Enumeration]

\definecounter[object][
  way=bysection,
  prefix=yes,
  prefixsegments=chapter:section,
]
\setupenumerations[
  counter=object,
]
\setupcaptions[
  counter=object,
]



\starttext

\dorecurse{4}{
  \chapter{Hi}
  \section{Knuth}
  \input knuth
  \dorecurse{3}{
    \enumeration
      \input zapf
      \par
    \placefigure{This is the caption}{This is some content}
  }
}

\stoptext