Need help on single stub matching problem.

I was reading part of a text book about designing input and output single stubs for an amplifier (https://www.google.com/url?sa=t&sour...thTkdoZ6LvgSh8) and look at example 14.8.1, if you look farther down the solutions they give the length of the input and output stubs (.1962*lamda and .1838*lamda) . How can you get stub lengths greater than 1/8 of a wavelength? If you look at a smith chart, and you line up the point from the unity immitance circle to y(short circuit), how can that length get any greater than 1/8 wavelength?

Not sure which design procedure you refer to. λ/8 stub corresponds to 90° rotation in Smith chart (|Xc| = ZL), range to mimic a capacitive reactance is 0 to λ/4 length open stub, you need L > λ/8 for |Xc| < ZL.

I should have made it more clear to my problem. How would you match a single stub (short circuit) with a load of 5.12+j7.54 with a characteristic impedance of 50 ohms? I tried to use the smith chart method. I first found d = 0.0247*lamda by calculating the distance toward the generator, the next step was to find l(length of stub) toward the load, do you get 0.1962*lamda and how? This is in reference to the problem.

I am confused about how to match the output of a transistor amplifier to a 50 ohm load using single stub matching on a smith chart. It is easy to figure out how to do a single stub match with a 50 ohm generator to the input of the amplifier, which I have found many resources on that, but when it is the opposite, I don't know what to do and I don't find any examples like this on the internet. Please help.

I think it may be done for s22 the same way as for s11.Or your difficulty is than s22 is influenced by matching network on s11 end?
You may try this program: http://fritz.dellsperger.net/smith.html
first press "keyboard" and add reflection coefficient
then press "line" (on the top-right)
finally press "os" (open stub)