you have to build the filter string using the rules of strings, and this string has to follow the filter rules.
sbreed is a string variable so you add it with & :
tbdog.filter("breed= " & sbreed )
The use of ' is in the case you put the string itself (not as a variable) in the filter, like
tbdog.filter("breed= 'Chiwawa' " )
to add an OR do this :
tbdog.filter("breed=" & sbreed & " OR name=" & sname)
Assuming breed and name are coulumn names, I don't know if this filter makes sense but the format should work.