Two liters is larger than two quarts. One liter is equivalent to approximately 1.05668821 US liquid quarts. Therefore, two liters would be approximately 2.11337642 US liquid quarts, which is greater than two quarts.
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Approximately, but not exact. A quart is a a bit less than a liter. One quart is a quarter (1/4) of a gallon; the quart used in the U.S. is equal to 0.946352946 liters. You can base your calculations on that.
Short answer: No. Slightly longer answer: A liter is a unit of volume in the Metric System that is equal to 1.05668 US fluid quarts. It's just a bit more than a quart.