With Access you need to use parentheses when doing more than one join:
SELECT *
FROM (Table1
INNER JOIN Table2
ON Table1.Master_Number = Table2.Master_Number)
INNER JOIN Table4
ON Table1.Master_Number = Table4.Master_Number;
This is essentiall spliting down you query so you have at most one join per section, i.e. Your First query is:
SELECT *
FROM Table1
INNER JOIN Table2
ON Table1.Master_Number = Table2.Master_Number;
Then you have:
SELECT *
FROM YourFirstQuery
INNER JOIN Table4
ON Table1.Master_Number = Table4.Master_Number;
This differs slightly from subqueries as you are still able to reference all fields from Table1 and Table2.
EDIT
To avoid duplicating columns you will need to explicitly list the columns you want (although you should be doing this anyway):
SELECT Table1.Master_Number,
Table1.Asset_Tag,
Table1.Serial_Number,
Table2.Last_Name,
Table2.First_Name,
Table4.Office_Number,
Table4.Location,
Table4.Department
FROM (Table1
INNER JOIN Table2
ON Table1.Master_Number = Table2.Master_Number)
INNER JOIN Table4
ON Table1.Master_Number = Table4.Master_Number;