Angular version 13
here is my code in .ts file
Declare th Array
  languages_array: Array<any> = [
{
  marathi_array: [
    {
      id: "marathi_speak", name: "marathi_speak", selected: false
    },
    {
      id: "marathi_write", name: "marathi_write", selected: false
    },
    {
      id: "marathi_read", name: "marathi_read", selected: false
    },
  ]
},
{
  hindi_array: [
    {
      id: "hindi_speak", name: "hindi_speak", selected: false
    },
    {
      id: "hindi_write", name: "hindi_write", selected: false
    },
    {
      id: "hindi_read", name: "hindi_read", selected: false
    },
  ]
},
{
  english_array: [
    {
      id: "english_speak", name: "english_speak", selected: false
    },
    {
      id: "english_write", name: "english_write", selected: false
    },
    {
      id: "english_read", name: "english_read", selected: false
    }
  ]
}
];
and i check the change event
  CheckBox(e: any, items: any) {
items.selected = e.target.checked
console.log(this.languages_array);
}
and in my .html file contain
<div class="col-md-12">
                <div class="table-responsive">
                  <table class="table table-hover table-bordered table-striped">
                    <thead>
                      <tr>
                        <th scope="col">Language</th>
                        <th scope="col">Speak</th>
                        <th scope="col">Write</th>
                        <th scope="col">Read</th>
                      </tr>
                    </thead>
                    <tbody class="text-center">
                      <tr>
                        <th> Marathi</th>
                        <td *ngFor="let item1 of languages_array[0].marathi_array; let i=index">
                          <input type="checkbox" (change)="CheckBox($event,item1)" [checked]="item1.selected">
                        </td>
                      </tr>
                      <tr>
                        <th> Hindi</th>
                        <td *ngFor="let item2 of languages_array[1].hindi_array; let i=index">
                          <input type="checkbox" (change)="CheckBox($event,item2)" [checked]="item2.selected">
                        </td>
                      </tr>
                      <tr>
                        <th> English</th>
                        <td *ngFor="let item3 of languages_array[2].english_array; let i=index">
                          <input type="checkbox" (change)="CheckBox($event,item3)" [checked]="item3.selected">
                        </td>
                      </tr>
                    </tbody>
                  </table>
                </div>
              </div>
and when you submit the form you can check this languages_array values using 
submit()
{
console.log(this.languages_array)
}