Calculating current for a parallel array of in-series LEDs
How much current flows through each branch of the circuit?

All branches are in parallel with the 12V source, so there is 12V across each branch.
$$12V = 6*V_{LED} + I_{BRANCH}*68\Omega$$
\$V_{LED}\$ is about 1.8V, so
$$1.2V = I_{BRANCH}*68 \Omega$$
$$\frac{1.2V}{68\Omega}=I_{BRANCH}\approx18mA$$

You have four identical branches each conducting the same magnitude of current, so the total current is about 4*18mA = 72mA. The tool you used gives a reasonable estimate.

If you accidentally used \$680\Omega\$ (Blue Grey Brown) resistors instead of \$68\Omega\$ (Blue Grey Black) resistors, the current will be 10% of the calculation above, giving around 8mA.