A family of Microsoft relational database management systems designed for ease of use.
If I understand correctly, I expect you would need a unique field in the first table (tblLinda). I added an autonumber field [ID].
Then create a cartesian/union query (qcarLinda) like:
SELECT ID, YearNum, [Year 1] AS TheValue
FROM tblLinda, TableX
WHERE [PeriodNum]=1
UNION ALL
SELECT ID,YearNum, [Year 2]
FROM tblLinda, TableX
WHERE [PeriodNum]=2
UNION ALL
SELECT ID,YearNum, [Year 3]
FROM tblLinda, TableX
WHERE [PeriodNum]=3;
Then create a crosstab based on qcarLinda:
TRANSFORM First(qcarLinda.TheValue) AS FirstOfTheValue
SELECT qcarLinda.ID
FROM qcarLinda
GROUP BY qcarLinda.ID
PIVOT qcarLinda.YearNum;