I can't read (the hands on) clocks.
It stands to reason that the speaker is referring to any time mechanism which uses the traditional 12-hour dial.
During the 15th and 16th centuries, the 12-hour analog dial and time
system gradually became established as standard throughout Northern
Europe for general public use. The 24-hour analog dial was reserved
for more specialized applications, such as astronomical clocks and
chronometers, and timetables, especially for railway and airline
travel.
Wikipedia suggests that the term clock face is used for both clocks and watches
A clock face or dial is the part of an analog clock (or watch) that
displays the time through the use of a fixed-numbered dial or dials
and moving hands. In its most basic form, recognized throughout the
world, the periphery of the dial is numbered 1 through 12 indicating
the hours in a 12-hour cycle, and a short hour hand makes two
revolutions in a day. A longer minute hand makes one revolution every
hour.
I suppose you could say: "I can't read twelve-hour dials" and be understood, but it's not very idiomatic.
EDIT
The expression read a clock is understood to mean watches and all mechanical clocks.
On a British reality show called "I'm A Celebrity... Get Me Out of Here!" one contestant confesed to not being able to tell the time.
... he earned himself some airtime by admitting that he didn’t know
how to read a clock-face. That didn’t matter, he insisted, because his
watch — reportedly worth £70,000 — was strictly for show, and anyway
it didn’t have any numbers on its dial. ‘It’s fashion,’ he says,
adding that it’s ‘much easier to look at your phone’.
Source Daily Mail
Ok, earlier today I was at a restaurant and some kids (maybe
highschool) asked what time it was so I pointed to a clock on the wall
and they stood there sort of silent. Then I heard one say to their
friends, "I'm really bad at telling time can you guys read it?"
Long story short none of them could read it but after a few minutes
they figured it out. Also now that I think about it, I have overheard
some teenagers talking about how they can't read a clock.
Source: www.neowin.net
Reading a Clock
Reading a clock takes practice, but after you learn how, it’s very easy to do! First, you’re going to locate the
hour hand. The hour hand is the shorter of the two clock hands.
Source: wikiHow to Read a Clock