This one return you total sum of all bills for each month (two fileds MonthID, Total):
var result = items.Where(b => b.Year == year)
.Select(b => new { b.MonthID, Total = b.Electricity + b.Gas + b.Phone + b.Water })
.GroupBy(b => b.MonthID)
.Select(g => new { MonthID = g.Key, Total = g.Sum(i => i.Total) });
And this one return sum of each bill for each month (five fields: MonthID, TotalElectricity, TotalPhone, TotalWater, TotalGas):
var result = items.Where(b => b.Year == year)
.GroupBy(b => b.MonthID)
.Select(
g => new {
MonthID = g.Key,
TotalElectricity = g.Sum(b => b.Electricity),
TotalPhone = g.Sum(b => b.Phone),
TotalWater = g.Sum(b => b.Water),
TotalGas = g.Sum(b => b.Gas)
}
);