How to optimize the query - Ef core

_context.Facilities will be enumerated (i.e. database will be called) for every iteration of previous loops. The quick fix is to call it ones and store results in variable:

var facilities = _context.Facilities.ToList();
foreach( var item in hotels.Items){
    foreach(var facility in item.HotelFacilities){
        foreach(var fac in facilities){
                        
            if(facility.FacilityCode == fac.Code){
                facility.HotelFacilityDescription = fac.Description;
            }
        }
    }
}

Next improvement can be converting facilities into Dictionary for searching purposes.

Even better approach can be writing query joining with _context.Facilities on database side (but here more info needed).

I've read this a couple times, but it looks like the relationship for Hotel.Facilities is a Facility, so could you not just do:

  HotelFacilities =  i.Facilities.ToList().Distinct().Take(6).Select(x => new HotelListHotelVm.HotelListFacilityVm {
                        Id = x.Id,
                        FacilityGroupCode = x.FacilityGroupCode,
                        HotelFacilityGroupDescription = x.FacilityGroup.Description,
                        FacilityCode = x.FacilityCode,
                        HotelFacilityDescription = x.Description
                    }),

If for some reason Hotel.Facilities is not pointing at a Facility, but is a Many-to-Many HotelFacilityGroup entity to a FacilityGroup, that also contains a FacilityCode, if the associated FacilityGroup has access to a set of Facilities beneath it you could leverage that:

Edit: It sounds like multiple Facilities share the same Code where some may have a null description. Provided that the facilities matching the code would be within the same facility group and not consider the same Code within different facility groups. If you need to match the code across all facilities then there probably isn't much of an alternative to loading the entire set of facility codes & descriptions.

  HotelFacilities =  i.Facilities.ToList().Distinct().Take(6).Select(x => new HotelListHotelVm.HotelListFacilityVm {
                        Id = x.Id,
                        FacilityGroupCode = x.FacilityGroupCode,
                        HotelFacilityGroupDescription = x.FacilityGroup.Description,
                        FacilityCode = x.FacilityCode,
                        HotelFacilityDescription = x.FacilityGroup.Facilities.Where(f => f.Code == x.FacilityCode && f.Description != null).Select(f => f.Description).FirstOrDefault()
                    }),

That would avoid the need to go load all of the facilities to resolve that code. Otherwise, if you do need to fetch across all facilities, pre-loading them would be the way to go, but rather than fetching the entire Facility entity I would recommend just the values you need, the Code and the Description. This cuts down on the amount of memory needed and potentially be a faster query:

var facilities = _context.Facilities
    .Select(f => new 
    {
        f.Code,
        f.Description
    }).ToList();

Edit: From there, finding a match using:

foreach( var facility in hotels.Items.SelectMany(x => x.HotelFacilities)
{
    facility.HotelFaciltyDescription = facilities
        .Where(x => x.Code == facility.FacilityCode 
            && !string.IsNullOrEmpty(x.Description)
        .Select(x => x.Description)
        .FirstOrDefault();
}

I would recommend an OrderBy clause to ensure the selection of the facility is predictable as it sounds like there could be multiple matches on a code with a non-null description.

The loop can be eliminated by projecting the value in the LINQ to Entities query.

It would have been quite easy if you had relationship and navigation property like other *Code fields. But as clarified in the comments, there is no such relationship, so you have to resort to old good manual left other join to emulate what navigation property provide automatically, e.g.

HotelFacilities = i.Facilities.ToList().Distinct().Take(6)
    // left outer join with Facilities
    .SelectMany(x => _context.Facilities
        .Where(f => x.FacilityCode == f.Code).DefaultIfEmpty(),
    (x, x_Facility) => new HotelListHotelVm.HotelListFacilityVm
    {
        Id = x.Id,
        FacilityGroupCode = x.FacilityGroupCode,
        HotelFacilityGroupDescription = x.FacilityGroup.Description,
        FacilityCode = x.FacilityCode,
        HotelFacilityDescription = x_Facility.Description // <--
    }),

Here x_Facility emulates optional reference navigation property x.Facility if existed.

In case you need just single property from the related table, instead of a left join you could also use the original query with single value returning correlated subquery inside the projection, e.g.

HotelFacilities = i.Facilities.ToList().Distinct().Take(6)
    .Select(x => new HotelListHotelVm.HotelListFacilityVm
    {
        Id = x.Id,
        FacilityGroupCode = x.FacilityGroupCode,
        HotelFacilityGroupDescription = x.FacilityGroup.Description,
        FacilityCode = x.FacilityCode,
        HotelFacilityDescription = _context.Facilities
            .Where(f => x.FacilityCode == f.Code)
            .Select(f => f.Description)
            .FirstOrDefault() // <--
    }),

or even

HotelFacilityDescription = _context.Facilities
    .FirstOrDefault(f => x.FacilityCode == f.Code).Description

All these will eliminate the need of the post loop executiong additional database queries. You can test them and take the one with best performance (#2 and #3 produce one and the same SQL, so it's a matter of taste - the choice is between #1 and #2/3).