<div class="box">
  <div class="slider-nav">
    <div class="slide-btn"><span>slide 1</span></div>
    <div class="slide-btn"><span>slide 2</span></div>
    <div class="slide-btn"><span>slide 3</span></div>
    <div class="slide-btn"><span>slide 4</span></div>
    <div class="slide-btn"><span>slide 5</span></div>
    <div class="slide-btn"><span>slide 6</span></div>
  </div
</div>

body {
  background-color: #ccc;
  margin: 0;
  padding: 0;
}

.box {
  position: relative;
  max-width: 80%;
  margin: 0 auto;
}

.slider-for {
  position: absolute;
  left: 0;
  right: 0;
  top: 0;
  z-index: 10;
}

.slide-container {
  height: 20vh;
  background-color: transparent;
  text-align: center;
  line-height: 20vh;
  font-size: 40px;
  font-weight: bold;
  border: 0;
  margin-bottom: 20px;
  box-sizing: border-box;
  
}

.decor {
  padding: 5px 40px;
  background-color: #fff;
  border: 2px solid #000
}

.slide-btn {
  text-align: center;
  box-sizing: border-box;
  height: 40vh;
  background-color: yellow;
  border: 1px solid #000;
  cursor: pointer;
  display: flex !important;
  align-items: flex-end;
  justify-content: center;
  padding-bottom: 20px;
  font-size: 30px;
  min-height: 120px;
  transition: .5s all;
}

.slick-active-first .slide-btn {
  background-color: red;
}

.slick-active-last .slide-btn {
  background-color: orange;
}

$('.slider-nav').slick({
  slidesToShow: 4,
  slidesToScroll: 1,
  dots: true,
  focusOnSelect: true
});

// On before slide change
$('.slider-nav').on('afterChange', function(event, slick, currentSlide, nextSlide){
  $('.slick-slide').removeClass('slick-active-first slick-active-last');
  $('.slick-active').eq(0).addClass('slick-active-first');
  $('.slick-active').eq(3).addClass('slick-active-last');
}).trigger('afterChange');

External CSS

  1. https://cdnjs.cloudflare.com/ajax/libs/slick-carousel/1.9.0/slick.min.css
  2. https://cdnjs.cloudflare.com/ajax/libs/slick-carousel/1.9.0/slick-theme.min.css

External JavaScript

  1. https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js
  2. https://cdnjs.cloudflare.com/ajax/libs/slick-carousel/1.9.0/slick.js