<ul>
  <li>
  <a href="">
  <img src="../../../img/goods/study.png" alt="学习">
  <img class="hide_tab" src="../../../img/goods/study_1.png" alt="学习">
  </a>
  </li>
  <li>
  <a href="">
  <img src="../../../img/goods/life.png" alt="生活">
  <img class="hide_tab" src="../../../img/goods/life_1.png" alt="生活">
  </a>
  </li>
  <li>
  <a href="" >
  <img src="../../../img/goods/sport.png" alt="运动">
  <img class="hide_tab" src="../../../img/goods/sport_1.png" alt="运动">
  </a>
  </li>
  <li>
  <a href="">
  <img src="../../../img/goods/clothes.png" alt="服饰">
  <img class="hide_tab" src="../../../img/goods/clothes_1.png" alt="服饰">
  </a>
  </li>
  <li>
  <a href="" >
  <img src="../../../img/goods/hat.png" alt="鞋帽">
  <imgclass="hide_tab" src="../../../img/goods/hat_1.png" alt="鞋帽">
  </a>
  </li>
  <li>
  <a href="" >
  <img src="../../../img/goods/food.png" alt="食品">
  <img class="hide_tab" src="../../../img/goods/food_1.png" alt="食品">
  </a>
  </li>
  <li>
  <a href="">
  <img src="../../../img/goods/other.png" alt="其他">
  <img class="hide_tab" src="../../../img/goods/other_1.png" alt="其他">
  </a>
  </li>
 </ul>

.right {
 float: left;
 ul {
 margin-left: 1px;
 li {
  display: inline-block;
  margin-left: 12px;
  width: 100px;
  height: 100px;
  a{
  position: relative;
  display: inline-block;
  width: 100px;
  height: 100px;
  .hide_tab{
  position: absolute;
  bottom: 0;
  }
  }
 }
 }
 }

data(){
 return{
 active: 0
 }
}

showActive(index) {
 this.active = index;
}

 <ul>
  <li>
  <a href="" @mouseenter="showActive(1)" @mouseleave="showActive(0)">
  <img src="../../../img/goods/study.png" alt="学习">
  <img v-show="active === 1" class="hide_tab" src="../../../img/goods/study_1.png" alt="学习">
  </a>
  </li>
  <li>
  <a href="" @mouseenter="showActive(2)" @mouseleave="showActive(0)">
  <img src="../../../img/goods/life.png" alt="生活">
  <img v-show="active === 2" class="hide_tab" src="../../../img/goods/life_1.png" alt="生活">
  </a>
  </li>
  <li>
  <a href="" @mouseenter="showActive(3)" @mouseleave="showActive(0)">
  <img src="../../../img/goods/sport.png" alt="运动">
  <img v-show="active === 3" class="hide_tab" src="../../../img/goods/sport_1.png" alt="运动">
  </a>
  </li>
  <li>
  <a href="" @mouseenter="showActive(4)" @mouseleave="showActive(0)">
  <img src="../../../img/goods/clothes.png" alt="服饰">
  <img v-show="active === 4" class="hide_tab" src="../../../img/goods/clothes_1.png" alt="服饰">
  </a>
  </li>
  <li>
  <a href="" @mouseenter="showActive(5)" @mouseleave="showActive(0)">
  <img src="../../../img/goods/hat.png" alt="鞋帽">
  <img v-show="active === 5" class="hide_tab" src="../../../img/goods/hat_1.png" alt="鞋帽">
  </a>
  </li>
  <li>
  <a href="" @mouseenter="showActive(6)" @mouseleave="showActive(0)">
  <img src="../../../img/goods/food.png" alt="食品">
  <img v-show="active === 6" class="hide_tab" src="../../../img/goods/food_1.png" alt="食品">
  </a>
  </li>
  <li>
  <a href="" @mouseenter="showActive(7)" @mouseleave="showActive(0)">
  <img src="../../../img/goods/other.png" alt="其他">
  <img v-show="active === 7" class="hide_tab" src="../../../img/goods/other_1.png" alt="其他">
  </a>
  </li>
 </ul>