**Core Concept**
The detection of pregnancy at 6 weeks gestation involves identifying the presence of a beta-human chorionic gonadotropin (β-hCG) hormone, which is produced by the placenta. The β-hCG hormone is crucial for maintaining the corpus luteum, ensuring continued progesterone production, and supporting embryonic development.

**Why the Correct Answer is Right**
The most accurate method to detect pregnancy at 6 weeks gestation is through a quantitative serum β-hCG assay. This method involves measuring the exact concentration of β-hCG in the blood. A serum β-hCG level of 25-50 mIU/mL is typically considered diagnostic of pregnancy at 6 weeks gestation. The high sensitivity and specificity of this test make it the gold standard for early pregnancy detection. The β-hCG hormone is produced by the placenta and is detectable in the blood as early as 6-8 days post-fertilization.

**Why Each Wrong Option is Incorrect**
* **Option A:** Urine pregnancy tests (UPTs) are less sensitive and less accurate than serum β-hCG assays, especially at 6 weeks gestation. They can produce false-negative results due to low β-hCG levels or false-positive results due to interferences.
* **Option B:** Ultrasound is a valuable diagnostic tool for confirming pregnancy and dating the gestation. However, it may not be able to detect the pregnancy at 6 weeks gestation, as the embryo is still very small and may not be visible.
* **Option D:** The progesterone level is not a reliable indicator of pregnancy at 6 weeks gestation. While progesterone is essential for maintaining pregnancy, its levels can fluctuate and may not accurately reflect the presence of a pregnancy.

**Clinical Pearl / High-Yield Fact**
Remember that a serum β-hCG level of 25-50 mIU/mL is typically considered diagnostic of pregnancy at 6 weeks gestation. This value is crucial for confirming pregnancy and ruling out ectopic pregnancy or other conditions that may mimic pregnancy.

**Correct Answer:** C.