First: 38 cm x 25 cm x 4 cm = 3800 cm³, which converts to 4.02 US liquid quarts, or 3.45 US dry quarts. For the term 'quart' liquid is the more popular used.
Remember that 1 US gallon (liquid) is equal to 3.7854 liters (almost 3800 cm³), and that 4 quarts is 1 gallon.
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approximately 2 quarts.
2.095 quarts for each inch deep (rounded)
The answer will depend on the depth of the pan. But since you have not bothered to provide that crucial bit of information, I cannot provide a more useful answer.
2.48 quarts (rounded) for each 1 inch deep in the pan
According to the bottom of my Pyrex 11 x 7 pan, it is equal to 2.2 quarts.