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Push = if you want to add any element to existing array you will do push method like 

const arr = ['First item', 'Second item', 'Third item'];
arr.push('Fourth item');
console.log(arr); // ['First item', 'Second item', 'Third item', 'Fourth item']


Assign Whole Array :
If you want to assign a complete to an index, inside an array you will do following. 

const mappingArr = {
    roleId: roleId,
    mappings: { moduleId: childModuleId, actionId: {} },
  };
mappingArr.mappings.actionId = newChecked;