I think your question could use some rephrasing, but maybe it’s just me… I’m going to take a guess that what you want is to output a <select> that has a selected option according to a variable you’re passing to your blade view, ¿correct?
If so, you have two options:
1. Ternary operators on each option, where you check if the variable is equal to the option’s value:

<select name="category" class="form-control">
   <option value="logo-design" {{ $header->category=="logo-design" ? 'selected' : '' }}>logo-design</option>
   <option value="website-development" {{ $header->category=="website-development" ? 'selected' : '' }}>website-development</option>
   <option value="app-development" {{ $header->category=="app-development" ? 'selected' : '' }}>app-development</option>
   <option value="search-engine-optimization" {{ $header->category=="search-engine-optimization" ? 'selected' : '' }}>search-engine-optimization</option>
   <option value="digital-marketing" {{ $header->category=="digital-marketing" ? 'selected' : '' }}>digital-marketing</option>
   <option value="cloud-hosting" {{ $header->category=="cloud-hosting" ? 'selected' : '' }}>cloud-hosting</option>
</select>

Or…
2. Use javascript to select it:

document.getElementById('select-category').value='{{ $header->category }}';

If you go for this, don’t forget to add an id to your select:

<select id="select-category" name="category" class="form-control">

I hope this helps.

I have to select auto option on edit blade which is getting data from table it’s not selecting the auto option on edit kindly help me with this code of edit blade is given below.

<label>Select Category</label>
<select name="category" class="form-control" selected="{{ $header->category }}">
  <option value="logo-design">logo-design</option>
  <option value="website-development">website-development</option>
  <option value="app-development">app-development</option>
  <option value="search-engine-optimization">search-engine-optimization</option>
  <option value="digital-marketing">digital-marketing</option>
  <option value="cloud-hosting">cloud-hosting</option>
</select>