You can use for..of syntax for iterating over the array elements. If the element has .name that you need, extract the .age:

function getAge(arr, name) {
    for (let s of students) {
        if (s.name == name) return s.age;
    }
}

Then you can use this function like this:

alert(getAge(students, 'Alex'));

Use Array.find to get the item in the array whose name property is "Alex", then get the item's age property:

var students=[{name:"Mary",age:10},{name:"Barbara",age:11},{name:"David",age:12},{name:"Alex",age:11}];

let res = students.find(e => e.name == "Alex").age
console.log(res)