Calculating current through resistor
Since someone else has provided an answer, I shall provide a more intuitive approach.

Since the two current sources are in parallel, combine the 2A and 1A sources into one 3A source and then you have the canonical current divider circuit.







simulate this circuit &ndash; Schematic created using CircuitLab

$$I_{R1} = 3A \dfrac{R_2}{R_1 + R_2} = 3A \dfrac{6}{3 + 6} = 2A $$

etc.