#### Answer

Total: 144 different orders.
Sample orders:
fish-peas-tea-cake
fish-peas-tea-pie

#### Work Step by Step

The number of ways in which a series of successive things can occur is found by multiplying the number of ways in which each thing can occur.
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1. The main course can be chosen in $4$ ways.
2. The vegetables can be chosen in $3$ ways.
3. The beverage can be chosen in $4$ ways.
4. The dessert can be chosen in $3$ ways.
Applying the Principle,
the total number of orders is $4\times 3\times 4\times 3=144$
Sample orders:
fish-peas-tea-cake
fish-peas-tea-pie