SQL Server Multiple Pivots
This works although I am not sure how to handle the date (sample is not a date):

Select DATENAME(month, [Date]) as 'date'
    , SUM(Case When Operator = 'Operator 1' then Invoice1 end) as 'Sum of Invoice 1 for Operator 1'
    , SUM(Case When Operator = 'Operator 1' then Invoice2 end) as 'Sum of Invoice 2 for Operator 1'
    , SUM(Case When Operator = 'Operator 2' then Invoice1 end) as 'Sum of Invoice 1 for Operator 2'
    , SUM(Case When Operator = 'Operator 2' then Invoice2 end) as 'Sum of Invoice 2 for Operator 2'
    , COUNT(distinct Client) as 'Count of Distinct Clients'
    , COUNT(distinct Entity) as 'Count of Distinct Entities'
From @data 
Group By [date];


Output:

date        | Sum of Invoice 1 for Operator 1   | Sum of Invoice 2 for Operator 1   | Sum of Invoice 1 for Operator 2   | Sum of Invoice 2 for Operator 2   | Count of Distinct Clients | Count of Distinct Entities
January     | 40                                | 50                                | 130                               | 140                               | 2                         | 4
February    | 60                                | 70                                | 160                               | 170                               | 2                         | 4


Your data (replaced by real dates):

Declare @data TABLE ([Date] datetime, Invoice1 int, Invoice2 int, Operator varchar(10), Client varchar(8), Entity varchar(10));
INSERT INTO @data(Date, Invoice1, Invoice2, Operator, Client, Entity)
VALUES
    ('20150101', 10, 15, 'Operator 1', 'Client 1', 'Entity A'),
    ('20150201', 20, 25, 'Operator 1', 'Client 1', 'Entity B'),
    ('20150101', 30, 35, 'Operator 1', 'Client 2', 'Entity C'),
    ('20150201', 40, 45, 'Operator 1', 'Client 2', 'Entity D'),
    ('20150101', 50, 55, 'Operator 2', 'Client 1', 'Entity E'),
    ('20150201', 70, 75, 'Operator 2', 'Client 2', 'Entity F'),
    ('20150101', 80, 85, 'Operator 2', 'Client 1', 'Entity G'),
    ('20150201', 90, 95, 'Operator 2', 'Client 2', 'Entity H')
;