The multiplicative model is:
Y = T * C * S * e

First we have to calculate the seasonal components.
Se = Y / TC

For quarterly time series we have to use a 4-Moving-Averages. These new series is the Trend-Cycle (we have then eliminated the seasonal component)

To get a seasonal component we have to divide the Demand (Y) with the Trend-Cycle (TC). We illustrate this with an example.

Moving average with a period of 4 have to be centered. We do this with averaging the MA-4 serie:
Centered_t= (MA4_t + MA4_t-1) / 2

To calculate the seasonal indexes:
Se = Y / TC
Se = Y_t / Centered_t = Unadjusted Seasonal Indexes

We have to adjust and smooth the seasonal indexes.

For quarters:
1: (0.629 + 0.600 + 0.589) / 3 = 0.606
2: (0.894 + 0.911 + 0.950) / 3 = 0.918
3: (0.989 + 1.014 + 0.971) / 3 = 0.992
4: (1.445 + 1.500 + 1.499) / 3 = 1.481

The sum of quarters (1, 2, 3 en 4) is 3.997
Adjust the seasonal factors so that it is equal to 4.0
The factor is (4.000 / 3.997)

The adjusted seasonal indexes are
1: 0.606
2: 0.919
3: 0.993
4: 1.482

We have found the seasonal indexes. Now we can calculate the Deseasonalized Trend-Cycle (TCe).

Y = TCSe
Y / S = TCe = Deseasonalized Trend-Cycle