I don't understand how to multiply bases.
Ex. 342 base 7
X 3 base 7
I understand that you can only use numbers 0,1,2,3,4,5,6 but I just have no idea what else to do. I don't get how to convert it to base 10.
It is exactly like multiplying in base ten, just remember where your arithmetic lives
$\displaystyle 3_7 \cdot 2_7=6_7$
Now the next one is just a bit harder
$\displaystyle 3_7 \cdot 4_7=15_7$ why is this true?
Remember that multiplication is just repeated addition i.e
$\displaystyle 4_7+4_7=11_7$ i.e we have 1 seven and one left over
$\displaystyle 11_7+4_7=15_7$
And for the last one we have
$\displaystyle 3_7\cdot 3_7=12_7$
Now when you multiply just use these compuations and don't forget to carry to the next column.
Also remember what base seven really means is
$\displaystyle 342_7=3\cdot 7^2+4\cdot 7^1+2\cdot 7^0$
This is just like base 10 i.e
$\displaystyle 342=3\cdot 10^2+4\cdot 10^1+2\cdot 10^0$
I hope this helps.