Answer for:

Layer2 switch

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You have HOST1 connected to SWITCH1 via a port that is in VLAN3. HOST2 is connected to SWITCH2 via a port that is in VLAN4. The switches are connected via a DOT1Q trunk and the native VLAN is 1. If that is correct, then why do you think the frame is sent untagged across the trunk? Since the port the frame came in on is in VLAN3 and VLAN1 is the native VLAN, the frame will be tagged with VLAN3 when it goes across the trunk. When SWITCH2 receives the frame, it sees the VLAN3 tag and will only forward it to a port in VLAN3. HOST2 is in VLAN4 and will never see the frame.