Show that product topology on Rd*R is metrizable..
(Rd is discrete topology on R.)
Nagata-Smirnov metrization theorem to show that a discrete topology on R is metrizable and use a Urysohn metrization theorem to show that a standard topology on R is metrizable.
Anyhow, to show that usual topology on R is metrizable, I recommend you to use Urysohn metrization theorem. It says that "Every second-countable regular Hausdorff space is metrizable." You need to verify that a standard(usual) topology on R is second countable and regular Hausdorff.