can a wireless router with 4 ports support 6 pc's in a household?

Be sure all 6 computers are set up for DHCP (get IP addresses automatically), and make sure the router is set up as a DHCP server. Each computer has to have its own IP, or you'll have collisions on the network. You could, alternatively, assign each computer a static IP from the router. Make sure each static IP is assigned to a different MAC.

Your wireless router can assign the ip to the host.

Find DHCP option on your router setting.

Set your pc to obtain the IP address with dynamic option.

Use hub or switch to extend the network or solving your router port limited.

Regards
http://yosellin.blogspot.com/

The router can support that number of computers, but the chances are the internet connection will start getting bogged down, especially if one or more persons is doing a download, streaming a video or otherwise getting a bunch of bandwidth.

Connect (wired) Modem to Router (wireless) to PCs.
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Set router POWER OFF.
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Reset modem: With a straightened paperclip, press RESET button momentarily.
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Wait 60 secs.
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Set router POWER ON.
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Reset router: With a straightened paperclip, press RESET button momentarily.
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Wait 60 secs.
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PC Command Line:
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Click [Start] - Click [Run...] - enter: cmd, Click [OK]
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At the prompt (c:\.....>) enter: ipconfig /release, press [ENTER]
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At the prompt (c:\.....>) enter: ipconfig /renew, press [ENTER]
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TEST: Connect to Internet.
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If SUCCESS: Repeat Steps after PC Command Line on your other PCs.
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If NO SUCCESS:
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At the prompt (c:\.....>) enter: ipconfig /all, press [ENTER]
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Ensure DHCP Enabled == YES
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If IP Address == 0.0.0.0 OR 169.254.0.0 to 169.254.255.255, connect PC (wired) to router (if possible) or modem and perform ALL steps again.
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the modem manufacturer intents up to 4 computers can be connected at once they will not support you trying to connect any more than that