I managed to get rid of that 406. Thanks, Ken. I omitted ,Accept Header, this time.
Now stuck some elsewhere.

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send request:
INVITE sip:1002@192.168.253.101;transport=udp SIP/2.0
Call-ID: ed05ada0e9aeb009a7b24eccd0678577@192.168.253.101
CSeq: 1 INVITE
From: <sip:1001@192.168.253.101>;tag=9782
To: <sip:1002@192.168.253.101>
Via: SIP/2.0/UDP 192.168.253.101:5073;branch=z9hG4bK1c1a8db63c4877132a77dacc5c931e99
Max-Forwards: 2
Contact: <sip:1001@192.168.253.101:5073;transport=udp>
Authorization: Digest username="1001",realm="192.168.253.101",uri="sip:192.168.253.101:5060",algorithm=MD5,opaque="",nonce="9b96327c-b094-11dd-b776-c14fb4e838dd",response="b425dde41cc093676705f0415344cf22"
Content-Type: application/sdp
Content-Length: 133

v=0
o=1001 920370 921739 IN IP4 192.168.253.101
s=-
c=IN IP4 192.168.253.101
t=0 0
m=audio 8756 RTP/AVP
a=rtpmap:0 PCMU/8000

received response:
SIP/2.0 100 Trying
Via: SIP/2.0/UDP 192.168.253.101:5073;branch=z9hG4bK1c1a8db63c4877132a77dacc5c931e99
From: <sip:1001@192.168.253.101>;tag=9782
To: <sip:1002@192.168.253.101>
Call-ID: ed05ada0e9aeb009a7b24eccd0678577@192.168.253.101
CSeq: 1 INVITE
User-Agent: FreeSWITCH-mod_sofia/1.0.trunk-9256M
Content-Length: 0


received response:
SIP/2.0 407 Proxy Authentication Required
Via: SIP/2.0/UDP 192.168.253.101:5073;branch=z9hG4bK1c1a8db63c4877132a77dacc5c931e99
From: <sip:1001@192.168.253.101>;tag=9782
To: <sip:1002@192.168.253.101>;tag=gB110DNg8jt5Q
Call-ID: ed05ada0e9aeb009a7b24eccd0678577@192.168.253.101
CSeq: 1 INVITE
User-Agent: FreeSWITCH-mod_sofia/1.0.trunk-9256M
Accept: application/sdp
Allow: INVITE,ACK,BYE,CANCEL,OPTIONS,PRACK,MESSAGE,SUBSCRIBE,NOTIFY,REFER,UPDATE,REGISTER,INFO,PUBLISH
Supported: 100rel,timer,precondition,path,replaces
Allow-Events: talk,presence,dialog,call-info,sla,include-session-description,presence.winfo,message-summary
Proxy-Authenticate: Digest realm="192.168.253.101",nonce="a40afd98-b094-11dd-b776-c14fb4e838dd",algorithm=MD5,qop="auth"
Content-Length: 0
--------

Although, I have included the authorization thingy in the INVITE request. Any idea, why its like that?

Thanks in advance.