Step 1: Recognize the diagnosis: an internal (transmesenteric) hernia has strangulated the small bowel, producing gangrene that must be resected and the ends rejoined.
Step 2: The favoured anastomotic method here is a single-layer technique using seromuscular Lembert sutures.
Step 3: The Lembert suture is an inverting stitch that approximates the serosa and muscularis without piercing the lumen, keeping the join clean; it may be placed continuous or interrupted.
Step 4: Choosing continuous closure merely for speed, using catgut, or a single layer that grabs the submucosa do not represent the recommended seromuscular Lembert approach. Hence the correct statement is the single-layer seromuscular Lembert anastomosis.
\[\boxed{\text{Single-layer seromuscular Lembert sutures}}\]