30 M distance should be fine for cat 6 cable , if your neighbors have a wireless router, then it's a straight forward of plugging the Ethernet cable from your Billion into their wireless router and configure the wireless security on their router and also turn DHCP off on that router, in the case of they wireless modem router, then you will need to put their modem router into AP(Access Point Mode) if that option is available on the modem router.
last word , you should be aware that sharing your internet connection this way might breach your internet providers terms and conditions.
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