loop object and then loop the array inside, here is a working example

https://codesandbox.io/s/eager-leaf-nx2mq?file=/src/App.vue

<template>
  <div id="app">
    <div v-for="(value, propertyName) in data" :key="propertyName">
      <h1>The key of the {{ propertyName }}</h1>
      <ul>
        <li v-for="(item, index) in data[propertyName]" :key="index">
          {{ item }}
        </li>
      </ul>
    </div>
  </div>
</template>

<script>
export default {
  name: "App",
  components: {},
  data() {
    return {
      data: {
        1: ["15-16", "16-17", "17-18", "18-19"],
        2: ["15-16", "16-17", "17-18", "18-19"],
      },
    };
  },
};
</script>

Try the below approach

var app = new Vue({
 el: '#app',
 data() {
  return {
   obj:{
    "1": [
        "15-16",
        "16-17",
        "17-18",
        "18-19"
    ],
    "2": [
        "15-16",
        "16-17",
        "17-18",
        "18-19"
    ]
   }
  };
 },
});

<script src="https://cdnjs.cloudflare.com/ajax/libs/vue/2.5.17/vue.js"></script>
<div id="app">
  <h1>Iterating the list</h1>
  <ul v-for="(item, attr) in obj" :key="attr"> Item {{attr}}
   <li v-for="(val, index) in item" :key="index">{{val}}</li>
  </ul>
</div>

in vue template you can loop through an object:

<template>
  <div>
    <div v-for="(value, key) in yourObject" :key="key">
      <h1>{{ key }}</h1>
      <ul>
        <li v-for="item in value" :key="'sub' + item">{{item}}</li>
      </ul>
    </div>
  </div>
</template>
<script>
export default {
  name: 'myComponent',
  data() {
    return {
      yourObject: {
        "1": [
          "15-16",
          "16-17",
          "17-18",
          "18-19"
        ],
        "2": [
          "15-16",
          "16-17",
          "17-18",
          "18-19"
        ]
      }
    }
  }
}
</script>
<style>
</style>

• you cant loop your root tag in a component so i put my loop in a div.
• remember to add key when you want to loop in your template. key must have a unique value.