Basically {{ $last= date('Y')-120 }}
in this part you are showing the value but you need to assign the value. So assign like this :
<?php $last= date('Y')-120; ?>
Same thing goes for the for loop too.Just compare the value. Do not put it in blade syntax.
<select id="year" name="year" class="form-control ">
{{ $last= date('Y')-120 }}
{{ $now = date('Y') }}
@for ($i = $now; $i >= $last; $i--)
<option value="{{ $i }}">{{ $i }}</option>
@endfor
</select>