Mancar vs. coxear
While both mancar and coxear describe the act of walking with difficulty due to pain or injury, the choice often depends on the region. Mancar is the dominant term in Brazilian Portuguese, whereas coxear is more frequently used in European Portuguese and can specifically emphasize the swaying motion of the hips.
Mancar
B1This is the general term for limping, meaning to walk unevenly because of a physical defect or temporary injury. In Brazilian Portuguese, mancar is the standard word used in almost all contexts.
O jogador saiu do campo mancando depois daquela falta.
(The player left the field limping after that foul.)
Ele começou a mancar porque o sapato estava muito apertado.
(He started to limp because the shoe was too tight.)
Não consigo andar sem mancar hoje.
(I cannot walk without limping today.)
Coxear
B2Derived from the word for thigh (coxa), this verb describes walking with a sway or listing to one side to avoid putting weight on a bad leg. It is the preferred term in Portugal and usually sounds slightly more formal or descriptive of the gait in Brazil.
O velho homem coxeava da perna esquerda.
(The old man was limping on his left leg.)
Ela sempre coxeia quando o tempo fica úmido.
(She always limps when the weather gets damp.)
Vi o cavalo coxear enquanto corria.
(I saw the horse limp while it was running.)
Summary
In essence, use mancar if you are speaking Brazilian Portuguese or want a general term for having a bad leg. Use coxear if you are speaking European Portuguese or want to describe the specific swaying motion associated with the limp.