Regarding Chapter 4, "Intimate and Family Murder" in the textbook The Will to Kill: Making Sense of Senseless Murder, how can I write a journal paragraph about the chapter? What does it tell us about family homicide or family annihilation?

Journal assignments usually comprise an introductory paragraph (which summarizes the text in question) followed by subsequent paragraphs that discuss your evaluation of the author's themes and conclusions.
In your question, you asked for help in writing a journal paragraph about Chapter 4. First, briefly summarize the essence of the chapter, using one or two sentences. Essentially, Chapter 4 encompasses the various motives and factors that contribute to murders in a domestic setting. List the types of murders discussed, such as patricide, matricide, infanticide, filicide, etc. How about crimes of passion perpetrated by mothers on those outside the immediate family circle (fetal abduction or kidnapping by Cesarean)? Later in the chapter, the authors discuss the emotional factors that lead to murder-suicides or other crimes of passion; they also discuss some preventive measures. 
After summarizing the chapter, use the rest of the paragraph to briefly discuss the author's conclusions. Do you agree with his interpretation of why mothers, fathers, husbands, wives, and children kill? Do you think the preventive measures are adequate? Should the perpetrators of the homicides be excused by the overwhelming emotional factors that compelled them to action? As for family homicide or annihilation, it seems that emotional factors play a large part in these acts. For example, jealousy is a prime motive, often exacerbated by economic factors such as unemployment or poverty. 
So, to write a journal paragraph of Chapter 4, your best bet would be to summarize the chapter in one or two sentences. Then, discuss the causative factors that lead to certain domestic homicides and whether you agree with the author's viewpoint about this. Next, include a few sentences (depending on how long you want the paragraph to be) about preventive measures and whether you think they will be effective.
 
http://www.sascv.org/ijcjs/pdfs/Webbbookreviewijcjs2012iindissue.pdf