Figure a place like Damascus shows resolve (8)
I believe the answer is:
tenacity
'resolve' is the definition.
(resolve can mean tenacity or determination)
'figure a place like damascus' is the wordplay.
'figure' becomes 'ten' (ten is a number or figure).
'place like damascus' becomes 'city' (Damascus is a Syrian city).
'ten'+'a'+'city'='TENACITY'
'shows' acts as a link.
(Other definitions for tenacity that I've seen before include "Perseverance in chosen course" , "Perseverance, doggedness" , "Staying power" , "Ability to stick firmly to task or position" , "Dogged resolve" .)