
All routers within their own AS has been configured with IGP, routers within their own AS are reachable to one another (imagine the above diagram is part of an AS network). The border routers are connected to each other AS and exchanging prefixes.
As shown in the diagram, two paths have different bandwidth, suboptimal routing is occurring. The requirement is to use 4mbps to reach the 172 networks (172.30.0.0/24 and 172.30.1.0/24), the remaining networks can use the default path as shown in show ip bgp command.
1841-2 to network 172.30.0.0/24 and 172.30.1.0/24 before path manipulation

Influence traffic destined for 172.30.0.0/24 and 172.30.1.0/24 to use 4mbps
1841-1#sh run | i access-list 1
access-list 1 permit 172.30.0.0 0.0.0.255
access-list 1 permit 172.30.1.0 0.0.0.255
1841-1(config)#do sh run | s route-map
route-map set-pref permit 10
match ip address 1
set local-preference 200
route-map set-pref permit 20
set local-preference 100
1841-1(config-router)#neighbor 3.3.3.3 route-map set-pref in
1841-1#clear ip bgp * soft
BGP table of 1841-2 still chose next-hop 4.4.4.4 as best path to 172 network

1841-2 does not have a route to 3.3.3.3 in RIB
1841-2#sh ip route | b Gateway
Gateway of last resort is not set
1.0.0.0/32 is subnetted, 1 subnets
O 1.1.1.1 [110/2] via 192.168.1.1, 02:50:48, FastEthernet0/0
2.0.0.0/32 is subnetted, 1 subnets
C 2.2.2.2 is directly connected, Loopback100
100.0.0.0/30 is subnetted, 1 subnets
C 100.1.10.4 is directly connected, Serial0/1/0
4.0.0.0/32 is subnetted, 1 subnets
S 4.4.4.4 [1/0] via 100.1.10.6
172.30.0.0/24 is subnetted, 2 subnets
B 172.30.0.0 [20/2] via 4.4.4.4, 00:08:45
B 172.30.1.0 [20/0] via 4.4.4.4, 00:30:53
10.0.0.0/24 is subnetted, 2 subnets
B 10.10.10.0 [20/2] via 4.4.4.4, 01:22:44
B 10.10.20.0 [20/0] via 4.4.4.4, 01:21:39
192.168.1.0/24 is variably subnetted, 2 subnets, 2 masks
O 192.168.1.1/32 [110/1] via 192.168.1.1, 02:50:48, FastEthernet0/0
C 192.168.1.0/24 is directly connected, FastEthernet0/0
C 192.168.2.0/24 is directly connected, Loopback2
O 192.168.3.0/24 [110/2] via 192.168.1.1, 02:49:37, FastEthernet0/0
1841-2#sh ip bgp 172.30.0.0
BGP routing table entry for 172.30.0.0/24, version 18
Paths: (2 available, best #2, table Default-IP-Routing-Table)
Advertised to update-groups:
2
200
3.3.3.3 (inaccessible) from 1.1.1.1 (1.1.1.1)
Origin IGP, metric 0, localpref 200, valid, internal
200
4.4.4.4 from 4.4.4.4 (4.4.4.4)
Origin IGP, metric 2, localpref 100, valid, external, best
1841-2#sh ip bgp 172.30.1.0
BGP routing table entry for 172.30.1.0/24, version 16
Paths: (2 available, best #2, table Default-IP-Routing-Table)
Advertised to update-groups:
2
200
3.3.3.3 (inaccessible) from 1.1.1.1 (1.1.1.1)
Origin IGP, metric 2, localpref 200, valid, internal
200
4.4.4.4 from 4.4.4.4 (4.4.4.4)
Origin IGP, metric 0, localpref 100, valid, external, best
So the reason the path was not chosen despite local preference was changed is because 3.3.3.3 is unreachable!
Neighbor <peer ip> next-hop-self command
1841-2(config)#router bgp 100
1841-2(config-router)#neighbor 1.1.1.1 next-hop-self
1841-1(config)#router bgp 100
1841-1(config-router)#neighbor 2.2.2.2 next-hop-self
1841-1 has a static route to 3.3.3.3 of 2651-1 but 1841-2 does not, the command is to modify the next-hop address of the sending router.
Path manipulation succeed!

Make sure the route is reachable by IGP within your own AS!
Verify reachability from 1841-2

1841-2#sh ip route bgp
172.30.0.0/24 is subnetted, 2 subnets
B 172.30.0.0 [200/0] via 1.1.1.1, 00:20:38
B 172.30.1.0 [200/2] via 1.1.1.1, 00:20:38
10.0.0.0/24 is subnetted, 2 subnets
B 10.10.10.0 [20/2] via 4.4.4.4, 01:46:00
B 10.10.20.0 [20/0] via 4.4.4.4, 01:44:55