Step 1: Line up the tubal sites from inside out.
Going from the uterus outward, a fallopian tube has an interstitial part inside the uterine wall, then a narrow isthmic part, then a wider ampullary part, and finally the fimbrial end near the ovary.
Step 2: Use wall thickness as the key idea.
A pregnancy growing in a thicker, more muscular, more stretchable wall survives longer before that wall gives way and ruptures. So the site with the most surrounding muscle wins in terms of how long the pregnancy can last.
Step 3: Rank the sites by that thickness.
The interstitial site is surrounded by the uterine muscle itself, the thickest and most stretchable tissue of all four sites, so it allows the longest growth, roughly 3 to 4 months. The ampullary site is wider than the isthmus but still only tubal wall, so it ruptures sooner, around 8 to 12 weeks. The isthmic site has a narrow, thin walled tube and tends to rupture earliest, near 6 to 8 weeks. The fimbrial end barely has any wall to stretch into, so a pregnancy there is usually lost into the abdomen very early.
Step 4: Conclude.
Because the uterine muscle around it can stretch the most, the interstitial ectopic pregnancy progresses for the longest time before rupture.
\[ \boxed{\text{Interstitial}} \]