Is an individual allowed to leave the country, even if they are unable to arrange for the declaration fee ? And the individaul is coming to the USA for work.

It's a SCAM!
There is NO such fee,

My friend is sent me a letter from Ghana immigration services indicating that she is required to have $4,000.00 to $6,000,00 dollars as a declaration fee for travel to the united states.. Could you confirm if this is indeed a requirement for travel.

Should have known it was Ghana.
This is a highly documented SCAM!!

My friend has sent me a picture of letter of declaration inquiring her to have in her position $4,000.00 to $6,000,00 dollars for travel out of ghana to the United states. Is this a requirement?

It's a very popular scam. Cut all ties. Google Ghana Romance Scam

No there is no such requiremet, and this is not a friend, it is a crook, who is trying to take your money.

It will be someone you meet online, most likely on a chat or date site. You have chatted about ? Two months, and they either got money from you for passport and visa, or they already had them and now is wanting this money.

Next it would not be a either or number, 4 to 6 thousand, it would be one number, more than 4000 or something.

And no, these are old facts, used by scam artists.
,
I have the pleasue of visiting one of them, some time ago. They were very proud of it.
A large office building, with people working 3 shifts. Extra help on the weekends.
Some do nothing but send out new emails to 1000's of people a day. Hopeing to get one to respond, if they do, it is handed over to the next group, who are better at getting people to pay. Next you seldom talk to the same person on email, but they use stock stories and stock answers, changed slightly by what you post.

If you start paying, another group takes over to help continue the scam.

Most photos are either stolen off internet, or they use photos of granddaughters, or young people in the area, they give a few dollars to, for their photo.

If web cams are used, they normally have a few pretty girls for this, and if pushed for web cam, they may even say, that they are sorry for fake photos, but they were of friend, and here is their real photos, and then they have the standard paid girls to do web cams.
In some cases the girls from photos work for them.
But they will have lots of reasons they can't always web cam,

If they keep getting the money, then it is airline tickets, and then they disapper for a week or two, and you worry, but then either they, but normally a "friend" emails you, telling you they are in the hospital or got arrested, and they need 5000 to 10000 for that,
There will always be more money, till you don't have any or till you figure it out