Unable to assign multiple checkbox selected values to a CDT

local!selectedLanguages is just the language number so you're trying to save a list of integer into a CDT without telling the save WHERE in the CDT you want to save it (as in, what field).

I'd do it like this:

a!localVariables(
  local!languages: {
    {
      languagenumber: 1,
      name: "English"
    },
    {
      languagenumber: 2,
      name: "Spanish"
    },
    {
      languagenumber: 3,
      name: "Telugu"
    }
  },
  local!selectedLanguages,
  local!employeelanguages, /*Using a local variable rather than rule input so that the code works when copy pasting*/
  a!formLayout(
    label: "Test" & index(
      local!employeelanguages,
      "languagenumber",
      {}
    ),
    contents: {
      a!checkboxField(
        label: "Languages Known",
        choiceLabels: index(local!languages, "name", null),
        choiceValues: index(local!languages, "languagenumber", null),
        value: index(
          local!employeelanguages,
          "languagenumber",
          {}
        ),
        saveInto: {
          local!selectedLanguages,
          a!save(
            target: local!employeelanguages,
            value: a!forEach(
              items: local!selectedLanguages,
              expression: {
                languageid: null,
                employeeid: loggedInUser(),
                languagenumber: fv!item
              }
            )
          )
        }
      ),
      a!paragraphField(
        value: local!employeelanguages
      )
    }
  )
)