**Core Concept**
The question tests the understanding of cellular biology, specifically protein synthesis and targeting. Proteins synthesized by ribosomes attached to the **rough endoplasmic reticulum (RER)** are generally destined for secretion or for insertion into cellular membranes.

**Why the Correct Answer is Right**
Proteins synthesized by **RER**-attached ribosomes have a signal sequence that directs them to the **RER** for initial processing. From the **RER**, these proteins can be further modified and sorted to various destinations, including the **Golgi apparatus**, lysosomes, and the plasma membrane.

**Why Each Wrong Option is Incorrect**
**Option A:** Incorrect because proteins destined for mitochondria are typically synthesized by free ribosomes and then transported into the mitochondria.
**Option B:** Incorrect because proteins destined for peroxisomes are also synthesized by free ribosomes and then transported into peroxisomes.
**Option D:** Incorrect because proteins destined for the cytosol are synthesized by free ribosomes.

**Clinical Pearl / High-Yield Fact**
Remember that proteins destined for the secretory pathway are synthesized by **RER**-attached ribosomes, which is crucial for understanding various cellular processes and diseases related to protein misfolding and trafficking.

**Correct Answer:** D. Lysosomes, Golgi apparatus, and plasma membrane are all potential destinations, but without the exact options, the most direct answer related to the RER's function would typically involve these organelles.