On page 69 of The TeXbook, there is a figure: 
On page 70 of The TeXbook, is says
Glue will never shrink more than its stated shrinkability. For example, the first glob of glue in our illustration will never be allowed to become narrower than 8 units wide, and TEX will never shrink the given horizontal list to make its total width less than 49 units.
How does the author calculate the shrink limits here?
shrink is specified in units, if you go \setlength\baselineskip{15pt minus 2pt} then the shrink is 2pt and the minimum size is 13pt It can also be infinite fil, fill or filll units so \vss for example is short for \vskip 0pt plus 1fil minus 1fil
Here is an example:
\def\ruleA{\vrule height1pt width45pt depth0pt} \def\ruleB{\vrule height1pt width30pt depth0pt} \noindent \vrule height1pt width100pt depth0pt\par \hbox to 100pt{\ruleA\hskip 20pt plus 4pt minus 15pt\ruleA} % case 1 \hbox to 100pt{\ruleA\hskip 20pt plus 4pt minus 10pt\ruleA} % case 2 \hbox to 100pt{\ruleA\hskip 20pt plus 4pt minus 3pt \ruleA} % case 3 \hbox to 100pt{\ruleB\hskip 20pt plus 4pt minus 3pt \ruleB} % case 4 \bye 
I have defined two rules (one width 45pt and the other 30pt). And I put the rules together with a glue in an horizontal box of width 100pt.
In cases 1-3, the total width of two rules is 90pt, so the glue should shrink 10pt since its natural width is 20pt.
Overfull \hbox (7.0pt too wide) detected at line 7 is raised.)In case 4, the glue is 20pt plus 4pt minus 3pt, which does not mean that the maximum width of the glue is 24pt. In fact, glue is allowed to stretch arbitrarily far, whenever it has a positive stretch component. And as you can see in the screenshot, the width of the last glue is 100pt-30pt*2 = 40pt (stretch amount is 20pt > 4pt). And this case gives an Underfull \hbox (badness 10000) warning.
The first glob of glue is space 9 stretch 3 shrink 1, so the narrowest that it can get is 9 − 1 = 8. (You might think that the widest is 9 + 3 = 12, but the text on page 70 immediately after the part that you quoted explains that this is not actually true and it can stretch wider.)
Adding up all of the widths and spaces, we get 5 + 9 + 6 + 9 + 3 + 12 + 8 = 52 as the natural width; but if we include the shrinks as well, then we get 5 + (9 − 1) + 6 + (9 − 2) + 3 + (12 − 0) + 8 = 49 as the narrowest that it can get.
So that is how 52, 8, and 49 are calculated. (The other numbers are just pulled out of a hat.)
The code below, can give you a visualization of what is happening. It is instructive to think of glue as springs, that can expand or shrink to arrange a set of boxes in other boxes. In the diagram below they are represented by the white spaces. YOu can observe that when the line width is 35mm and TeX is building a paragraph box4 is dropped down onto a second line. At 49mm it just fits. The figure is rendered by inserting the boxes in a tabular. Experiment with changing the values. To calculate manually all the glues add the positive together and the negative together, to obtain the stretchability or shrinkability.
\documentclass{article} \usepackage{array,xcolor} \fboxsep=0pt\fboxrule=0pt \NewDocumentCommand\Fbox{m m} { \colorbox{cyan}{\hbox to#1{box$_#2$\strut}} } \parindent0pt \setlength\arraycolsep{0pt} \long\def\maketable#1{\par\leavevmode \begin{tabular}{l|@{}p{#1}@{}|@{}} #1 &\Fbox{14mm}{1}\hskip\skipa \Fbox{15mm}{2}\hskip\skipb \Fbox{8mm}{3}\hskip \skipc \Fbox{8mm}{4} \end{tabular} \smallskip } % set the skips \newskip \skipa \newskip \skipb \newskip \skipc \skipa=0mm plus 3mm minus 1mm \skipb=0mm plus6mm minus 2mm \skipc=0mm plus0mm minus 0mm \begin{document} %make the tables \maketable{35mm} \maketable{49mm} \maketable{52mm} \maketable{55mm} \end{document} 