permit作动词意为“允许”“准许”＝allow someone to do or something to happen
permit to do
eg. I cannot permit this to happen.我不能允许此事发生. The rules of the club do not permit alcohol.俱乐部规定不许饮酒.
permit作名词意为“许可证”
admit 动词 指（通常不情愿地）承认、供认
eg.Few politicians admit their mistakes.政客很少会承认自己的错误. She will never admit that she is wrong.她绝对不会承认自己做错了.
allow意为“允许”“准许”“容许”“承认”(正式）
eg.As a child,I was never allowed to stay up late.小时候,大人从不允许我熬夜.
至于accept的用法如下：
accept
vt.
1.接受；收下
to accept a present from his friend
接受朋友的礼物
I've received a gift from him, but I'm not going to accept it.
我收到了他送的礼物,但是我不准备接受.
Please accept my apologies.
请接受我的歉意.
2.承认；同意
承担责任
to accept the blame
承担责任
3.承兑；认付