Multiply two lists

a = {1, 2, 3};
b = {4, 5, 6};
Flatten[KroneckerProduct[a, b]]

{4, 5, 6, 8, 10, 12, 12, 15, 18}

Use DeleteDuplicates to, well, delete duplicates.

DeleteDuplicates @ Flatten @ Outer[Times, a, b] 

{4, 5, 6, 8, 10, 12, 15, 18}

Also, shorter but much slower

DeleteDuplicates[Times @@@ Tuples @ {a, b}]

{4, 5, 6, 8, 10, 12, 15, 18}

Note: If speed is a concern, then Outer, KroneckerProduct and TensorProduct are much faster than Table and Tuples methods:

SeedRandom[1]
{a, b} = RandomInteger[100, {2, 1500}];
r1 = DeleteDuplicates @ Flatten @ Outer[Times, a, b]; // RepeatedTiming // First

0.0103

r2 = DeleteDuplicates[Times @@@ Tuples @ {a, b}]; // RepeatedTiming // First 

0.92

r3 = DeleteDuplicates[Flatten[Table[i*j, {i, a}, {j, b}]]]; // RepeatedTiming // First  

0.78

r4 = DeleteDuplicates @Flatten[KroneckerProduct[a, b]]; // RepeatedTiming // First   

0.011

r5 = DeleteDuplicates[Flatten[TensorProduct[a, b]]]; // RepeatedTiming // First

0.011

r1 == r2 == r3 == r4 == r5

True

Another way to produce the result you seek is:

DeleteDuplicates[Flatten[Table[i*j, {i, a}, {j, b}]]]

{4, 5, 6, 8, 10, 12, 15, 18}

This will also work, and generalizes easily to more than two lists:

DeleteDuplicates[Flatten[TensorProduct[a, b]]]

TensorProduct runs in time similar to KronekerProduct and Outer.