Interpreting formulas with $\Sigma \Sigma$ (two sigma)

This notation has the following meaning: consider real numbers $a_{ij}$, where $i$ ranges from 1 to 3, and $j$, from 1 to 2. We thus have the following equality:

$$\sum_{i=1}^3 \sum_{j=1}^2 a_{ij}=\sum_{i=1}^3(a_{i1}+a_{i2})=(a_{11}+a_{12})+(a_{21}+a_{22})+(a_{31}+a_{32}).$$

There is nothing more to it. However, as Davide pointed out, sometimes you can simplify the computations - but this highly depends on the nature of the number $a_{ij}$ (for example, they might satisfy a recurrence relation).

To evaluate the double sum, first, expand the inner summation and then continue by computing the outer summation

$$\sum_{i=1}^4 \sum_{j=1}^3 ij = \sum_{i=1}^4(i + 2i +3i) = \sum_{i=1}^4 6i = 6 + 12 + 18 + 24 = 60$$