if skillId is a variable and assuming that SkillsList contains a property called Id. Then the following would work in getting you any data that has the specified skillId.
var list = this._viewModel.Data.Where(t=>t.SkillsList.Any(s=>s.Id == skillId));
If Skillslist is just an array of integers then the following would work.
var list = this._viewModel.Data.Where(t=>t.SkillsList.Any(s=> s == skillId));
Now if you are checking against a list the following would work.
var list = this._viewModel.Data.Where(t=>t.SkillsList.Any(s=> skillsList.contains(s));