You will find the following hints useful to improve your writing skills and speech. It is a guide to modern English usage.

Accidentaly or accidentally?

The correct adverb of 'accident' is 'accidentally'.

The school laboratory accidentally caught fire.

Accommodate or accomodate?

This word is often misspelt. Remember that there are two 'c's and two 'm's in 'accommodate.'

The auditorium can accommodate 1,000 guests.

Achilles' heel or achilles heel?

Achilles' heel is a weak point or small fault, especially in somebody's character which can be used or attacked by other people to their advantage.

Vanity is his Achilles' heel.

However modern writers seem to prefer 'achilles heel.'

Acknowledgement or acknowledgment?

Although both words are admissible, modern writers prefer 'acknowledgement'?

He has quoted Shakespeare without acknowledgement.

Administer or administrate?

Administer is the correct form. It means 'to control the affairs of a business, an organisation.'

A committee has been appointed to administer the project.

Admission or admittance?

Both words come from 'admit' but they are used in different ways.

He is a coward by his own admission.

The police found it difficult to gain admittance to the house.