Let's draw the scenario to better understand the problem:
It appears that AB = AC + CB.
Using the relationship, let's find AC.
[tex]\text{ AB = AC + CB}[/tex][tex]32\text{ = AC + 1}4[/tex][tex]32-14\text{ = AC + 1}4\text{ - 14}[/tex][tex]\text{ 18 = AC }\rightarrow\text{ AC = 18 cm}[/tex]Therefore, the length of AC = 18 cm.