You can make a local variable and save totals there, then just return total value

function addObjValue(arr) {
    let total = 0
    arr.forEach(element => {
        const val = element.value;
        total += checkObjValue(val);
        console.log(total);
    })
    return total
}

And after that make your sum equal to returned value

sum = addObjValue(myArr);

Update One more thing. To get sum from an array you can use reduce method

arr.reduce((totalSum, currenElement) => {
    return totalSum + currenElement.value
}, 0 /*first value of totalSum (by default equal to the first element of the array)*/)

Issue:

• total is scoped under addObjValue so it doesn't add to final sum
• break inside switch-case is unreachable as it comes after return 1;

You can make below 2 changes to make it work.

let sum = 0;
const myArr = [{name: 'dj', value: '2'}, {name: 'kd', value: '3'}];

function addObjValue(arr, total) {
    arr.forEach(element => {
        const val = element.value;
        total += checkObjValue(val);
    })
    return total; // change 1: returning total
}

function checkObjValue(x) {
    switch(x) {
        case '2':
            return 1;
        case '3':
            return 5;
    }
}

sum = addObjValue(myArr, sum); // change 2: assigned return value back to sum