O engenheiro desenha a nova linha do metro com cuidado para não estragar o plano.

In European Portuguese, it’s common to include the definite article before a profession or role.

• O engenheiro literally means “the engineer.”
• Omitting the article (just Engenheiro desenha…) sounds more like a headline or very informal note.
• In everyday sentences, keep o/a before professions even when you’re not specifying a particular person.

Desenha is the 3rd person singular of desenhar in the present indicative. It matches ele/ela/você.
Present indicative of desenhar:

• Eu desenho
• Tu desenhas
• Ele/ela/você desenha
• Nós desenhamos
• Vós desenhais
• Eles/elas/vocês desenham

The noun linha is feminine singular, so the article is a. Even with an adjective, European Portuguese typically retains the article:

• a linha → a nova linha
  If you omit the article, it’s possible but more poetic or journalistic:
• (Newspapers) Nova linha do metro abre hoje.

Do is the contraction of de + o. Since metro is masculine singular with a definite article, you must combine them:

• de + o metro → do metro
  Without the article, you’d say linha de metro in a very generic sense, but here we’re referring to the metro line.

Com cuidado literally means “with care” → “carefully.” Alternatives:

• cuidadosamente (more formal)
• com atenção (“with attention”)
• de modo cauteloso (formal/written)

Para não + infinitive expresses purpose: “in order not to…”

• para não estragar o plano = “so as not to ruin the plan.”
  Alternative with subjunctive:
• para que não estrague o plano (more formal, uses subjunctive estrague).
  Both are correct, but para não + infinitive is more common in speech.

Estragar means “to spoil,” “to ruin,” or “to damage.” It’s a transitive verb, so it usually takes a direct object without a preposition:

• estragar o plano (“ruin the plan”)
  If you need to specify damage to something:
• estragar algo (“to spoil something”)