4. \(4\sqrt{3t}-\sqrt{12t}+2\sqrt{75t}\)

При \(t\geqslant0\):

\(\sqrt{12t}=2\sqrt{3t}\), \(\sqrt{75t}=5\sqrt{3t}\).

Тогда:

\(4\sqrt{3t}-2\sqrt{3t}+2\cdot5\sqrt{3t}=12\sqrt{3t}\).

Ответ: \(12\sqrt{3t}\)