Dezesseis vs. dezasseis
The words dezesseis and dezasseis both mean sixteen in Portuguese. The difference between them is not in meaning, but in spelling and pronunciation, corresponding to the two main variants of the language: Brazilian Portuguese and European Portuguese.
Dezesseis
A1This is the standard spelling and pronunciation for the number sixteen (16) in Brazilian Portuguese. The second e is pronounced clearly.
Eu tenho dezesseis anos de idade.
(I am sixteen years old.)
O meu time marcou dezesseis pontos no primeiro tempo.
(My team scored sixteen points in the first half.)
Ela comprou dezesseis brigadeiros para a festa.
(She bought sixteen brigadeiros for the party.)
A sala de aula tem capacidade para dezesseis alunos.
(The classroom has capacity for sixteen students.)
O voo para o Rio de Janeiro é o de número dezesseis.
(The flight to Rio de Janeiro is number sixteen.)
Dezasseis
A1This is the standard spelling and pronunciation for the number sixteen (16) in European Portuguese. In this variant, the a is pronounced, and the preceding e is often silent or unstressed.
O meu irmão faz dezasseis anos para a semana.
(My brother turns sixteen next week.)
Preciso de dezasseis euros para comprar o bilhete de comboio.
(I need sixteen euros to buy the train ticket.)
A encomenda chegará dentro de dezasseis dias úteis.
(The order will arrive within sixteen business days.)
A morada dele é na Rua da Liberdade, número dezasseis.
(His address is on Liberdade Street, number sixteen.)
Comemos dezasseis sardinhas assadas no São João.
(We ate sixteen grilled sardines at the São João festival.)
Summary
In essence, the choice between dezesseis and dezasseis depends entirely on the geographical variant of Portuguese you are using. Use dezesseis when writing or speaking Brazilian Portuguese, and use dezasseis for European Portuguese. Both words mean sixteen and are perfectly understood by speakers of either variant, but using the correct form for your context will make your Portuguese sound more natural.